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Allen Tannenbaum - One of the best experts on this subject based on the ideXlab platform.
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on the optimal solutions in spectral Commutant lifting theory
Journal of Functional Analysis, 1991Co-Authors: Hari Bercovici, Ciprian Foias, Allen TannenbaumAbstract:Abstract In this note we give a property of the optimal solutions to the spectral Commutant lifting theorem of H. Bercovici, C. Foias, and A. Tannenbaum ( Trans. Amer. Math. Soc. , in press) which shows that such solutions are spectral analogues of inner functions which appear as optimal solutions in classical dilation theory.
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a spectral Commutant lifting theorem
Transactions of the American Mathematical Society, 1991Co-Authors: Hari Bercovici, Ciprian Foias, Allen TannenbaumAbstract:©1991 American Mathematical Society. First published in Transactions of the American Mathematical Society, Vol. 325, No. 2, June 1991 by the American Mathematical Society
Jingbo Xia - One of the best experts on this subject based on the ideXlab platform.
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a double Commutant relation in the calkin algebra on the bergman space
Journal of Functional Analysis, 2017Co-Authors: Jingbo XiaAbstract:Abstract Let T be the Toeplitz algebra on the Bergman space L a 2 ( B , d v ) of the unit ball in C n . We show that the image of T in the Calkin algebra satisfies the double Commutant relation: π ( T ) = { π ( T ) } ″ . This is a surprising result, for it is the opposite of what happens in the Hardy-space case [16] , [17] .
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on the essential Commutant of the toeplitz algebra on the bergman space
Journal of Functional Analysis, 2017Co-Authors: Jingbo XiaAbstract:Let TT be the C⁎C⁎-algebra generated by the Toeplitz operators {Tf:f∈L∞(B,dv)}{Tf:f∈L∞(B,dv)} on the Bergman space of the unit ball. We show that the essential Commutant of TT equals {Tg:g∈VObdd}+K{Tg:g∈VObdd}+K, where VObddVObdd is the collection of bounded functions of vanishing oscillation on B and KK denotes the collection of compact operators on La2(B,dv).
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on the essential Commutant of
Transactions of the American Mathematical Society, 2008Co-Authors: Jingbo XiaAbstract:Let T(QC) (resp. T) be the C * -algebra generated by the Toeplitz operators {T φ : φ ∈ QC} (resp. {T φ : φ ∈ L∞}) on the Hardy space H 2 of the unit circle. A well-known theorem of Davidson asserts that T(QC) is the essential Commutant of T. We show that the essential Commutant of T(QC) is strictly larger than T. Thus the image of T in the Calkin algebra does not satisfy the double Commutant relation. We also give a criterion for membership in the essential Commutant of T(QC).
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coincidence of essential Commutant and the double Commutant relation in the calkin algebra
Journal of Functional Analysis, 2003Co-Authors: Jingbo XiaAbstract:Let B be a von Neumann algebra on a separable Hilbert space H. We show that, if the dimension of B as a linear space is infinite, then it has a proper C∗-subalgebra A whose essential Commutant in B(H) coincides with the essential Commutant of B. Moreover, if π is the quotient map from B(H) to the Calkin algebra B(H)/K(H), then π(A)≠π(B) and {π(A)}″=π(B).
Zhe Liu - One of the best experts on this subject based on the ideXlab platform.
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a double Commutant theorem for murray von neumann algebras
Proceedings of the National Academy of Sciences of the United States of America, 2012Co-Authors: Zhe LiuAbstract:Abstract Murray–von Neumann algebras are algebras of operators affiliated with finite von Neumann algebras. In this article, we study commutativity and affiliation of self-adjoint operators (possibly unbounded). We show that a maximal abelian self-adjoint subalgebra of the Murray–von Neumann algebra associated with a finite von Neumann algebra is the Murray–von Neumann algebra , where is a maximal abelian self-adjoint subalgebra of and, in addition, is . We also prove that the Murray–von Neumann algebra with the center of is the center of the Murray–von Neumann algebra . Von Neumann’s celebrated double Commutant theorem characterizes von Neumann algebras as those for which , where , the Commutant of , is the set of bounded operators on the Hilbert space that commute with all operators in . At the end of this article, we present a double Commutant theorem for Murray–von Neumann algebras.
Serguei Shimorin - One of the best experts on this subject based on the ideXlab platform.
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Commutant lifting and factorization of reproducing kernels
Journal of Functional Analysis, 2005Co-Authors: Serguei ShimorinAbstract:Abstract A general version of the Commutant lifting theorem for operators between different spaces is proved. It includes as special cases the lifting theorems of Ball–Trent–Vinnikov and Volberg–Treil. A multivariable variant of the Volberg–Treil theorem is obtained as a corollary. A certain factorization property of reproducing kernels is shown to be a sufficient condition for the lifting. Another factorization property is shown to be a necessary condition.
Aaron Tikuisis - One of the best experts on this subject based on the ideXlab platform.
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relative Commutant pictures of roe algebras
Communications in Mathematical Physics, 2019Co-Authors: Jan Spakula, Aaron TikuisisAbstract:AT was supported by EPSRC EP/N00874X/1. JS was supported by Marie Curie FP7-PEOPLE-2013-CIG Coarse Analysis (631945). We would like to thank Ulrich Bunke, Alexander Engel, John Roe, Thomas Weighill, Stuart White, and Rufus Willett for comments and discussion relating to this piece.
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relative Commutant pictures of roe algebras
arXiv: Operator Algebras, 2017Co-Authors: Jan Spakula, Aaron TikuisisAbstract:Let X be a proper metric space, which has finite asymptotic dimension in the sense of Gromov (or more generally, straight finite decomposition complexity of Dranishnikov and Zarichnyi). New descriptions are provided of the Roe algebra of X: (i) it consists exactly of operators which essentially commute with diagonal operators coming from Higson functions (that is, functions on X whose oscillation tends to 0 at infinity) and (ii) it consists exactly of quasi-local operators, that is, ones which have finite epsilon propogation (in the sense of Roe) for every epsilon>0. These descriptions hold both for the usual Roe algebra and for the uniform Roe algebra.