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## Filters

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Continuity of linear operators commuting with shifts

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 ...

##
###
On the classification of binary shifts of finite commutant index

1999
*
Proceedings of the National Academy of Sciences of the United States of America
*

We provide a complete classification up to conjugacy of

doi:10.1073/pnas.96.26.14700
pmid:10611276
pmcid:PMC24711
fatcat:zyeb77ftdzbc5nbi3iwcyoignm
*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. ...##
###
An operator not satisfying Lomonosov's hypothesis

1980
*
Journal of Functional Analysis
*

Partial results suggesting that

doi:10.1016/0022-1236(80)90073-7
fatcat:bm4nszvbe5ew7fi4oaszmzmrdm
*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. ...##
###
Equal-Time Commutators and Electromagnetic Mass Splittings

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? ...

##
###
Strictly Cyclic Weighted Shifts

1971
*
Proceedings of the American Mathematical Society
*

Nordgren recently showed that certain weighted

doi:10.2307/2038136
fatcat:l5dqwgavenhazf3q6wqzthprhu
*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*). ...##
###
Continuous shift commuting maps between ultragraph shift spaces

2019
*
Discrete and Continuous Dynamical Systems. Series A
*

In this work we characterize

doi:10.3934/dcds.2019043
fatcat:oxzwbdxzovfxvbar74msxw3umm
*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. ...##
###
Toral and spherical Aluthge transforms of 2-variable weighted shifts
[article]

2016
*
arXiv
*
pre-print

Finally, we briefly discuss

arXiv:1611.00115v1
fatcat:b2roydbgibgolm6riy37iss4my
*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. ...##
###
A class of shifts on the hyperfinite ${\rm II}\sb 1$ factor

1990
*
Proceedings of the American Mathematical Society
*

We construct

doi:10.1090/s0002-9939-1990-1013966-x
fatcat:u72pj3xxknhb5nkqpvgt5kvob4
*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* ...##
###
Aluthge Transforms of 2-Variable Weighted Shifts

2018
*
Integral equations and operator theory
*

Fourth, we study how

doi:10.1007/s00020-018-2475-1
fatcat:zc3x6qohcvfbjla5t2uloytz3y
*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]. ...##
###
On the pole-shifting problem for non-commutative rings

1991
*
Linear Algebra and its Applications
*

Certainly (

doi:10.1016/0024-3795(91)90109-a
fatcat:5nbkgtkk45b7jik4r4sizabn7i
*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 ...##
###
Shifts on the HyperfiniteII1Factor

1998
*
Journal of Functional Analysis
*

Powers has constructed a family of unital endomorphisms of

doi:10.1006/jfan.1997.3225
fatcat:nrrwijfdxbbt3kwnzuafukn5cm
*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. ...##
###
On the classification of binary shifts of minimal commutant index

1999
*
Proceedings of the National Academy of Sciences of the United States of America
*

We provide a complete classification up to conjugacy of

doi:10.1073/pnas.96.16.8839
pmid:10430857
pmcid:PMC17694
fatcat:v7npsdybpfbezawv7itxttfq7m
*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*. ...##
###
An answer to a question of A. Lubin: The lifting problem for commuting subnormals
[article]

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. ...

##
###
On Commutators in Algebras of Unbounded Operators

1988
*
Zeitschrift für Analysis und ihre Anwendungen
*

More speci/ically,

doi:10.4171/zaa/278
fatcat:2fpspzx5tfcdtec7icqvfk7l3u
*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). ...##
###
High-Performance Low-Power FFT Cores

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. ...

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