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Self-consistency: a fundamental concept in statistics

Thaddeus Tarpey, Bernard Flury
<span title="">1996</span> <i title="Institute of Mathematical Statistics"> Statistical Science </i> &nbsp;
We generalize this concept to self-consistent random vectors: a random vector Y is self-consistent for X if ‫ޅ‬ X Y = Y almost surely.  ...  We provide some general results on self-consistent random variables, give examples, show relationships between the various methods, discuss a related notion of self-consistent estimators and suggest directions  ...  ACKNOWLEDGMENTS The authors would like to thank the Editor, a referee, Nicola Loperfido and Ann Mitchell for constructive comments on earlier versions of this article.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1214/ss/1032280215">doi:10.1214/ss/1032280215</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cxerobsywze2xlojdu4vzghbhq">fatcat:cxerobsywze2xlojdu4vzghbhq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180721081604/https://corescholar.libraries.wright.edu/cgi/viewcontent.cgi?article=1047&amp;context=math" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/23/2e/232e474782b1d381d1e7a1d55370ea872bd9360c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1214/ss/1032280215"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

A group algebra construction of binary even self dual codes

J Wolfmann
<span title="">1987</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
We give a construction of binary doubly even self dual codes as binary images of some principal ideals in a group algebra.  ...  In particular, we show how to produce such a code starting from any binary cyclic code with length not a multiple of 4 and dimension at least 3. * The results of this paper were presented at IEEE Symposium  ...  This identification will be used consistently in the following. Then the principal ideal (x) generated by x in .4 is called an H-code. Theorem (Camion). An H-code C is self-dual (C = C±).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0012-365x(87)90213-5">doi:10.1016/0012-365x(87)90213-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2keljxys5jbxnlx4yglqk3vq24">fatcat:2keljxys5jbxnlx4yglqk3vq24</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170925234233/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/32e/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS8wMDEyMzY1eDg3OTAyMTM1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a8/7a/a87aba0af65f4b359810b29824ab1e754fc4e6b0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0012-365x(87)90213-5"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Principal points and elliptical distributions from the multivariate setting to the functional case

Juan Lucas Bali, Graciela Boente
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/rwdjnin7wvc3xmoc6by27vqkgq" style="color: black;">Statistics and Probability Letters</a> </i> &nbsp;
In this paper, we generalize the concepts of principal points, self-consistent points and elliptical distributions so as to fit them in this functional framework.  ...  The k principal points of a random vector X are defined as a set of points which minimize the expected squared distance between X and the nearest point in the set.  ...  The following Theorems provide the desired result relating, for elliptical elements, self-consistency and principal components. Theorem 3.2.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.spl.2009.05.016">doi:10.1016/j.spl.2009.05.016</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/erlropmyzfe67kulqflkbnydpm">fatcat:erlropmyzfe67kulqflkbnydpm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200903103721/https://arxiv.org/pdf/2006.04188v1.pdf" title="fulltext PDF download [not primary version]" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/6a/8a/6a8ab179bc6c110a45599d67a62cabd8071b1a44.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.spl.2009.05.016"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Local resolvents of operators with one-dimensional self-commutator

Constantin Apostol, Kevin Clancey
<span title="1976-01-01">1976</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/a64sw4kcsveajhudnssdwrwvze" style="color: black;">Proceedings of the American Mathematical Society</a> </i> &nbsp;
In this note the following theorem is proven: Theorem. // there exists a real number p such that ess inf EH < p < ess sup EH and fE \t -p\ dt < oo, then the operator T has a nontrivial invariant subspace  ...  It is not known at present whether every operator with a one-dimensional self-commutator has a nontrivial invariant subspace.  ...  On the other hand ||(jd(A)|| < 1, for X G a(T). This implies that <p(X) is not analytic in any neighborhood of A0 (see, e.g. Dunford and Schwartz [5, p. 220]).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9939-1976-0410418-5">doi:10.1090/s0002-9939-1976-0410418-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dnprv3yckjhxpm7pb7pm5tkltu">fatcat:dnprv3yckjhxpm7pb7pm5tkltu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190504095418/https://www.ams.org/journals/proc/1976-058-01/S0002-9939-1976-0410418-5/S0002-9939-1976-0410418-5.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/cd/e6/cde65d09508f8a75bf0601d8a09f98fdfb37ba8b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9939-1976-0410418-5"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Local Resolvents of Operators with One-Dimensional Self-Commutator

Constantin Apostol, Kevin Clancey
<span title="">1976</span> <i title="JSTOR"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/a64sw4kcsveajhudnssdwrwvze" style="color: black;">Proceedings of the American Mathematical Society</a> </i> &nbsp;
In this note the following theorem is proven: Theorem. // there exists a real number p such that ess inf EH < p < ess sup EH and fE \t -p\ dt < oo, then the operator T has a nontrivial invariant subspace  ...  It is not known at present whether every operator with a one-dimensional self-commutator has a nontrivial invariant subspace.  ...  On the other hand ||(jd(A)|| < 1, for X G a(T). This implies that <p(X) is not analytic in any neighborhood of A0 (see, e.g. Dunford and Schwartz [5, p. 220]).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2041377">doi:10.2307/2041377</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zb7tqajl55hsnm7umgrqnj5fhy">fatcat:zb7tqajl55hsnm7umgrqnj5fhy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180725054950/http://www.ams.org/journals/proc/1976-058-01/S0002-9939-1976-0410418-5/S0002-9939-1976-0410418-5.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/cc/21/cc21af2082b113650f2aaf3a4460b1255ea14b88.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2041377"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> jstor.org </button> </a>

Elliptic Operators in Subspaces and the Eta Invariant

Anton Savin, Bert-Wolfgang Schulze, Boris Sternin
<span title="">2002</span> <i title="Portico"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/v7ctld52kzg2dgbdhqzzd3276a" style="color: black;">K-theory</a> </i> &nbsp;
The method used to obtain the corresponding formula is based on the index theorem for elliptic operators in subspaces obtained in 1], 2].  ...  The paper deals with the calculation of the fractional part of theinvariant for elliptic self-adjoint operators in topological terms.  ...  fractional part of the functional d in terms of the principal symbol of the subspace and the other of the -invariant via the principal symbol of a self-adjoint operator.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1023/a:1021684908461">doi:10.1023/a:1021684908461</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/iogiaafapzha7mh4dllkasl5vi">fatcat:iogiaafapzha7mh4dllkasl5vi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922230606/https://publishup.uni-potsdam.de/opus4-ubp/frontdoor/deliver/index/docId/2342/file/99_14.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1f/3f/1f3fa05510de6492bbf9a35cc88936490cfcd868.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1023/a:1021684908461"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Page 565 of Mathematical Reviews Vol. 14, Issue 6 [page]

<span title="">1953</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
the type of a potential ; Spaces L, and W,; Embedding theorems; General methods of norming W,“ and consequences of an embedding theorem; Some consequences of embedding theorems; Complete con- tinuity  ...  This theorem is called the S.0.M. theorem because it represents a generalization of the following theorem, due to U. Sasaki and J. Ogasawara [J. Sci. Hiroshima Univ. Ser.  ... 
<span class="external-identifiers"> </span>
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Dimensionality Reduction with Subspace Structure Preservation [article]

Devansh Arpit, Ifeoma Nwogu, Venu Govindaraju
<span title="2016-04-06">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications.  ...  Our key contribution is to show that 2K projection vectors are sufficient for the independence preservation of any K class data sampled from a union of independent subspaces.  ...  We show that for K independent subspaces, 2K projection vectors are sufficient for independence preservation (theorem 2).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1412.2404v3">arXiv:1412.2404v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/axchj5a5hbdpneglf6upg6we54">fatcat:axchj5a5hbdpneglf6upg6we54</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200914054530/https://arxiv.org/pdf/1412.2404v3.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/bf/1e/bf1effd4aec097ab836b1ed50d21a6ed0740ae6c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1412.2404v3" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Parabolic Subgroups of Real Direct Limit Groups [article]

Elizabeth Dan-Cohen, Ivan Penkov, Joseph A. Wolf
<span title="2009-01-02">2009</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Let G_R be a classical real direct limit Lie group and g_R its Lie algebra. The parabolic subalgebras of the complexification g_C were described by the first two authors.  ...  This also gives a description of the parabolic subgroups of G_R. Furthermore, we give a geometric criterion for a parabolic subgroup P_C of G_C to intersect G_R in a parabolic subgroup.  ...  Conversely assume (i) and (ii). From (i), G R ∩ P C is a parabolic subgroup of G R , and from (ii), where Tr p C denotes the set of infinite trace conditions described in Definition 2.6.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0901.0295v1">arXiv:0901.0295v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/m6zwuj2amrhbfcc6nic6u3pttq">fatcat:m6zwuj2amrhbfcc6nic6u3pttq</a> </span>
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Local conditions for critical and principal manifolds

Umut Ozertem, Deniz Erdogmus
<span title="">2008</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2omreisfsje33bgvx3orrdifre" style="color: black;">Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing</a> </i> &nbsp;
A subspace-constrained xed-point algorithm is proposed to determine the principal graph.  ...  We present local conditions for critical and principal manifolds by introducing the concept of subspace local maxima.  ...  smoothness and self consistency constraints for the nonlinear solutions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/icassp.2008.4518004">doi:10.1109/icassp.2008.4518004</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/icassp/OzertemE08.html">dblp:conf/icassp/OzertemE08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/oibqsiwmxrchpf53ejuiu2q2jm">fatcat:oibqsiwmxrchpf53ejuiu2q2jm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20110623144226/http://indigo.ece.neu.edu/~erdogmus/publications/C120_ICASSP2008_PrincipalSurfaces_Umut.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/16/1c/161c5c15ec80d13665e920542caede56e793a626.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/icassp.2008.4518004"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Spectral Sections [article]

Marina Prokhorova
<span title="2021-11-22">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In the first part of the paper we generalize results of Melrose and Piazza to arbitrary base spaces, not necessarily compact.  ...  The paper is devoted to the notion of a spectral section introduced by Melrose and Piazza.  ...  Ivanov for useful remarks and suggestions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2008.04672v5">arXiv:2008.04672v5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/x7deyar6gnam7lwacm6jaqbo2q">fatcat:x7deyar6gnam7lwacm6jaqbo2q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20211201194200/https://arxiv.org/pdf/2008.04672v5.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/79/e0/79e01268a9d0b92e4ac079870a1a530d06076aef.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2008.04672v5" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Alternative proof of the a priori tan Θ theorem

A. K. Motovilov
<span title="">2016</span> <i title="Pleiades Publishing Ltd"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3vtcll2q3ne6bd2nln5mxh3ul4" style="color: black;">Theoretical and mathematical physics</a> </i> &nbsp;
Let A be a self-adjoint operator in a separable Hilbert space.  ...  It is known that if V<√(2) dist(σ_0,σ_1), then the spectrum of the perturbed operator L=A+V consists of two disjoint parts ω_0 and ω_1 which originate from the corresponding initial spectral subsets σ_  ...  Let A be a self-adjoint operator on a separable Hilbert space H, and let the spectrum of A consist of a two isolated components σ 0 and σ 1 which satisfy the condition (1.1).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1134/s0040577916010074">doi:10.1134/s0040577916010074</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vxpfv2nzdzf2zamypcc23srgva">fatcat:vxpfv2nzdzf2zamypcc23srgva</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200905084413/https://arxiv.org/pdf/1510.02316v1.pdf" title="fulltext PDF download [not primary version]" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/0c/14/0c14c471f12d12dcb43d911819568e7f23580315.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1134/s0040577916010074"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Page 30 of Mathematical Reviews Vol. 22, Issue 1A [page]

<span title="">1961</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Theorem 4 can be extended to non-separable B by showing that for any closed separable subspace M of B, the property (E) holds with «=0 and L a one-dimensional subspace of M*; the author’s method will then  ...  Suppose N is a (real or complex) normed linear space and L a subspace (not necessarily closed) of N*.  ... 
<span class="external-identifiers"> </span>
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Gottlieb's theorem for F-fibrations

Petar Pavešić
<span title="">2001</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hp7o5f6pmrg57k2m46s4syavf4" style="color: black;">Topology and its Applications</a> </i> &nbsp;
We prove a generalization to F-fibrations of Gottlieb's theorem about the total space of universal fibrations.  ...  We will illustrate the theorem with a simple example.  ...  Then H = SO(n + 1) and H * = SO(n), so by the above theorem BSO(n) ESO(n + 1) × SO(n+1) S n and the fibration S n → BSO(n) → BSO(n + 1) classifies SO(n + 1)-bundles with fibre S n .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0166-8641(00)00010-9">doi:10.1016/s0166-8641(00)00010-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/o67y7ttzxnbufnelvpz3k4hzda">fatcat:o67y7ttzxnbufnelvpz3k4hzda</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171005042334/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/ec8/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDE2Njg2NDEwMDAwMDEwOQ%3D%3D.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/08/f9/08f9b5334023c7c22b7163025fec0e3a0b03be34.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0166-8641(00)00010-9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

An Invariant for Certain Operator Algebras

R. W. Carey, J. D. Pincus
<span title="1974-05-01">1974</span> <i title="Proceedings of the National Academy of Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nvtuoas5pbdsllkntnhizy4f4q" style="color: black;">Proceedings of the National Academy of Sciences of the United States of America</a> </i> &nbsp;
The connection of the principal function, under additional hypothesis, with the determination of the maximal ideal space of the C* algebra generated by T is discussed, and it is shown that the principal  ...  function, even when it takes noninteger values, plays a role in establishing the existence of invariant subspaces for T and in determining the point spectrum of T.  ...  Theorem 6 gives a somewhat more general result.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1073/pnas.71.5.1952">doi:10.1073/pnas.71.5.1952</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/16592156">pmid:16592156</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC388361/">pmcid:PMC388361</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/trzavpybojfijnal6nuwajfmw4">fatcat:trzavpybojfijnal6nuwajfmw4</a> </span>
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