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Continuity of linear operators commuting with shifts

Richard J Loy
1974 Journal of Functional Analysis  
The continuity of linear operators T : E + F satisfying the commutativity condition TT, = T,T has been considered in [lo] and [l 11.  ...  On the negative side the analogous result fails for the FrCchet spaces C(R), Cm(R) even supposing T commutes with all translations ([lo]).  ...  attained on (i) T commutes with all shifts (ii) T is continuous and commutes with all shifts (iii) T is continuous and commutes with d$erentiation (iv) T commutes with convolution, that is, T is a perfect  ... 
doi:10.1016/0022-1236(74)90003-2 fatcat:lzvs27vslzepnd6ck2dgxpcd7m

On the classification of binary shifts of finite commutant index

G. L. Price
1999 Proceedings of the National Academy of Sciences of the United States of America  
We provide a complete classification up to conjugacy of the binary shifts of finite commutant index on the hyperfinite II 1 factor.  ...  There is a natural correspondence between the conjugacy classes of these shifts and polynomials over GF(2) satisfying a certain duality condition. conjugacy class subfactor index  ...  We provide a complete classification up to conjugacy of the binary shifts of finite commutant index on the hyperfinite II 1 factor.  ... 
doi:10.1073/pnas.96.26.14700 pmid:10611276 pmcid:PMC24711 fatcat:zyeb77ftdzbc5nbi3iwcyoignm

An operator not satisfying Lomonosov's hypothesis

D.W Hadwin, E.A Nordgren, Heydar Radjavi, Peter Rosenthal
1980 Journal of Functional Analysis  
Partial results suggesting that the answer to this question was negative were obtained by many authors: see [2, 4, II] and the references given there.  ...  An obvious C to consider is the unilateral shift.  ...  Hence p[+ -4(h)]-l =m Ii& is in H2(p), and so is Clearlvf == [n/l, -+(h)]g, which completes the proof. LEMMA 3.  ... 
doi:10.1016/0022-1236(80)90073-7 fatcat:bm4nszvbe5ew7fi4oaszmzmrdm

Equal-Time Commutators and Electromagnetic Mass Splittings

David G. Boulware, S. Deser
1968 Physical Review  
The relation between electromagnetic mass shifts (or splittings) to order a and equal time commutators is analysed.  ...  The relation is then more complicated even if the commutators still exist.  ...  ii) Under what conditions are the mass shifts and equal time commutators related? A third question -what determines the mass shifts when the commutators do not exist?  ... 
doi:10.1103/physrev.175.1912 fatcat:heod27avlnatfa6trxfsi35zau

Strictly Cyclic Weighted Shifts

Alan Lambert
1971 Proceedings of the American Mathematical Society  
Nordgren recently showed that certain weighted shift operators on Hubert space have the property that they commute with no unbounded closed densely defined linear transformations.  ...  After establishing some tests for the existence of such a strictly cyclic vector, several further examples are given of weighted shift operators satisfying Nordgren's commutativity property.  ...  ;The purpose of this paper is to give necessary and sufficient conditions for a shift Sa to have property (i) and to show every shift with property (i) also has property (ii).  ... 
doi:10.2307/2038136 fatcat:l5dqwgavenhazf3q6wqzthprhu

Continuous shift commuting maps between ultragraph shift spaces

Daniel Gonçalves, Marcelo Sobottka
2019 Discrete and Continuous Dynamical Systems. Series A  
In this work we characterize the class of continuous shift commuting maps between these spaces.  ...  In particular, we prove a Curtis-Hedlund-Lyndon type theorem and use it to completely characterize continuous, shift commuting, length preserving maps in terms of generalized sliding block codes.  ...  The authors thank the referee for the careful review of the manuscript.  ... 
doi:10.3934/dcds.2019043 fatcat:oxzwbdxzovfxvbar74msxw3umm

Toral and spherical Aluthge transforms of 2-variable weighted shifts [article]

Raul E. Curto, Jasang Yon
2016 arXiv   pre-print
Finally, we briefly discuss the relation between spherically quasinormal and spherically isometric 2-variable weighted shifts.  ...  We introduce two natural notions of Aluthge transforms (toral and spherical) for 2-variable weighted shifts and study their basic properties.  ...  The authors are deeply indebted to the referee for several helpful comments that improved the presentation.  ... 
arXiv:1611.00115v1 fatcat:b2roydbgibgolm6riy37iss4my

A class of shifts on the hyperfinite ${\rm II}\sb 1$ factor

Donald Bures, Hong Sheng Yin
1990 Proceedings of the American Mathematical Society  
We construct and classify up to conjugacy certain shifts on the hyperfinite IIx-factor, each being a shift of Jones index n which fails to be an «-shift.  ...  In particular for each prime n we construct uncountably many such shifts.  ...  By [2] , provided 5 is a shift on G and co is nondegenerate, the data G, s, co give rise to a shift o = o(G, s, co) on the hyperfinite II,-factor R realized as the twisted group von Neumann algebra W*  ... 
doi:10.1090/s0002-9939-1990-1013966-x fatcat:u72pj3xxknhb5nkqpvgt5kvob4

Aluthge Transforms of 2-Variable Weighted Shifts

Raúl E. Curto, Jasang Yoon
2018 Integral equations and operator theory  
Fourth, we study how the Taylor and Taylor essential spectra of 2-variable weighted shifts behave under the toral and spherical Aluthge transforms; as a special case, we consider the Aluthge transforms  ...  of the Drury-Arveson 2-shift.  ...  Preliminary versions of some of the results in this paper have been announced in [31] . Some of the calculations in this paper were obtained using the software tool Mathematica [49].  ... 
doi:10.1007/s00020-018-2475-1 fatcat:zc3x6qohcvfbjla5t2uloytz3y

On the pole-shifting problem for non-commutative rings

James Brewer, Lee Klingler
1991 Linear Algebra and its Applications  
Certainly (ii) implies (iii). If (iii) holds, then (ii) follows immediately by taking v to be the last row of the matrix L. Thus, conditions (ii) and (iii) are equivalent.  ...  They prove a positive result for this ring and apply it, via a clever trick, to deduce a dynamic pole-shifting result for the (commutative) subring of the above ring consisting of all continuous real-valued  ... 
doi:10.1016/0024-3795(91)90109-a fatcat:5nbkgtkk45b7jik4r4sizabn7i

Shifts on the HyperfiniteII1Factor

Geoffrey L Price
1998 Journal of Functional Analysis  
Powers has constructed a family of unital endomorphisms of the hyperfinite II 1 factor R. The range of each Powers shift _ is a subfactor of index 2 in R.  ...  A cocycle conjugacy invariant for a Powers shift is its commutant index, i.e., the first index k for which the range of _ k has a nontrivial relative commutant in R.  ...  ACKNOWLEDGMENTS The author is grateful to Sigmund Vik for a careful reading of the manuscript, to Alexis Alevras for pointing out an error in the original manuscript, and to Robert T.  ... 
doi:10.1006/jfan.1997.3225 fatcat:nrrwijfdxbbt3kwnzuafukn5cm

On the classification of binary shifts of minimal commutant index

G. L. Price
1999 Proceedings of the National Academy of Sciences of the United States of America  
We provide a complete classification up to conjugacy of the binary shifts of commutant index 2 on the hyperfinite II 1 factor.  ...  There is a natural correspondence between the conjugacy classes of these shifts and polynomials over GF(2) satisfying a certain duality condition.  ...  In this paper we consider those binary shifts with commutant index 2, the minimal possible commutant index (3) and show that there are countably many such shifts.  ... 
doi:10.1073/pnas.96.16.8839 pmid:10430857 pmcid:PMC17694 fatcat:v7npsdybpfbezawv7itxttfq7m

An answer to a question of A. Lubin: The lifting problem for commuting subnormals [article]

Sang Hoon Lee, Woo Young Lee, Jasang Yoon
2015 arXiv   pre-print
The subnormality for the sum of commuting subnormal operators does not guarantee the existence of commuting normal extensions.  ...  We now claim that (T 1 , T 2 ) is subnormal ⇐⇒ 0 < x ≤ 2 11 . (2.8) Towards (2.8) , observe that the commutativity of T 1 and T 2 comes directly from Figure 1 (ii).  ...  Figure 1 . 1 (i) The weight diagram of a generic 2-variable weighted shift; (ii) The weight diagram of the 2-variable weighted shift (T 1 , T 2 ) given in Theorem 1.1. (T 1 , T 2 ) | M∩N §4.  ... 
arXiv:1406.6450v3 fatcat:aj4m7xdksvagfd7vbnjxkf5spi

On Commutators in Algebras of Unbounded Operators

Werner Timmermann
1988 Zeitschrift für Analysis und ihre Anwendungen  
More speci/ically, ii 2) € (I), then T is a commutator it and only ii(1,,) is shi It-admissible and T-addable. A € . (2) ) be an operator with Tr A = 0. Is then A a commutator?  ...  ., S = (So) an operator on X with SI E (X0), E IIS II < do. Then S = LW -WL where W = (W) is defined by (6) Here L is the left shift. Ii case S = Da (6) is equivalent to (4).  ... 
doi:10.4171/zaa/278 fatcat:2fpspzx5tfcdtec7icqvfk7l3u

High-Performance Low-Power FFT Cores

Wei Han, Ahmet T. Erdogan, Tughrul Arslan, Mohd. Hasan Hasan
2008 ETRI Journal  
The results show that up to 38% and 55% power savings can be achieved by the proposed pipelined FFTs and parallel-pipelined FFTs respectively, compared to the conventional pipelined FFT processor architectures  ...  Different combinations of hybrid low-power techniques are exploited to reduce power consumption, such as multiplierless units which replace the complex multipliers in FFTs, low-power commutators based  ...  Therefore, the operation saving of additions/subtractions is 28.8%, and that of shift is 14.3%. Figure 5 shows the shift-and-add module for the three constants in a 16-point FFT.  ... 
doi:10.4218/etrij.08.0107.0189 fatcat:vsawkfqvmzg5jo6lm7et6wcar4
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