Contributed talks session A (Tuesday)Copyright (c) 2022 Washington University in St. Louis All rights reserved.
https://openscholarship.wustl.edu/iwota2016/Contributed/contributedtalksTuesdayA
Recent Events in Contributed talks session A (Tuesday)en-usWed, 02 Feb 2022 13:05:31 PST3600An extension of the Beurling-Chen-Hadwin-Shen theorem for noncommutative Hardyspaces associated with finite von Neumann algebras
https://openscholarship.wustl.edu/iwota2016/Contributed/contributedtalksTuesdayA/5
https://openscholarship.wustl.edu/iwota2016/Contributed/contributedtalksTuesdayA/5Tue, 19 Jul 2016 15:00:00 PDT
In 2015, Yanni Chen, Don Hadwin and Junhao Shen proved a noncommutative version of Beurling's theorem for a continuous unitarily invariant norm α on a tracial von Neumann algebra (M,τ)such that α is one dominating with respect to τ. The role of H^∞ is played by a maximal subdiagonal algebra A . In the talk, we first will show that if α is a continuous normalized unitarily invariant norm on (M,τ), then there exists a faithful normal tracial state ρ on M and a constant c >0 such that α is a c times one norm-dominating norm on (M,ρ). Moreover, ρ (x)= τ (xg), where x in M, g is positive in L^1 (Z,τ), where Z is the center of M . Here c and ρ are not unique. However, if there is a c and ρ so that the Fuglede-Kadison determinant of g is positive, then Beurling-Chen-Hadwin-Shen theorem holds for L^(α ) (M,τ). The key ingredients in the proof of our result include a factorization theorem and a density theorem for for L^(α ) (M,ρ).
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Wenjing LiuToral m-isometric tuples of commuting operators on a Hilbert space
https://openscholarship.wustl.edu/iwota2016/Contributed/contributedtalksTuesdayA/4
https://openscholarship.wustl.edu/iwota2016/Contributed/contributedtalksTuesdayA/4Tue, 19 Jul 2016 16:00:00 PDT
We initiate the study of toral m-isometric tuples of commuting operators on a Hilbert space. This class of operator naturally generalize the m-isometry of a single operator in Agler and Stankus's work. The word "toral" is in contrast to the "spherical" m-isometric tuple of several commuting operators studied in by Gleason and Richter. We derive some basic reproducing formulas and give some alternative characterizations for this class of operators. Spectral and decomposition properties are obtained. In particular, we construct numerous examples of toral m-isometric tuples by using sums of operators, product of operators, functions of operators. Concrete examples of tuples of weighted shifts and multiplication operators on holomorphic spaces of several variables are displayed.
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Caixing GuComposition C*-algebras Induced by Linear-fractional Non-automorphism Self-maps of the Unit Disk
https://openscholarship.wustl.edu/iwota2016/Contributed/contributedtalksTuesdayA/3
https://openscholarship.wustl.edu/iwota2016/Contributed/contributedtalksTuesdayA/3Tue, 19 Jul 2016 15:30:00 PDT
If $\varphi$ is an analytic self-map of the unit disk $\mathbb{D}$, then the composition operator $C_{\varphi}: f \mapsto f \circ \varphi$ is a bounded operator on the Hardy space $H^2(\mathbb{D})$. We are particularly interested in composition operators induced by linear-fractional self-maps of $\mathbb{D}$. Several authors have investigated the structures of C$^*$-algebras generated by these operators and either the unilateral shift or the ideal of compact operators on $H^2(\mathbb{D})$. For non-automorphism self-maps of the disk, these structure results have required restrictions on the behavior of the inducing maps on the unit circle. In this talk, we relax these restrictions and investigate the structures of $C^*$-algebras generated by the ideal of compact operators and arbitrary finite collections of composition operators induced by linear-fractional, non-automorphism self-maps of $\mathbb{D}$.
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Katie QuertermousComplex Symmetric Composition Operators on $H^2$
https://openscholarship.wustl.edu/iwota2016/Contributed/contributedtalksTuesdayA/1
https://openscholarship.wustl.edu/iwota2016/Contributed/contributedtalksTuesdayA/1Tue, 19 Jul 2016 14:30:00 PDT
Garcia has motivated much interest in complex symmetric operators. He and Hammond initiated the search for composition operators exhibiting complex symmetry, with only one example so far: involutive disk automorphisms. In this talk, we give new examples of linear-fractional maps that induce complex symmetric composition operators and also identify the conjugation that induces the complex symmetry. Joint work with Sivaram Narayan and Daniel Sievewright of Central Michigan University.
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Derek Thompson