Problems and Recent Methods in Operator Theory.

Cover -- Title page -- Contents -- Preface -- From Helgermites to Lipschitz: Remembering Jim Jamison -- References -- A Mazur-Ulam theorem for normed gyrolinear spaces -- 1. Introduction -- 2. Normed gyrolinear spaces -- 3. A Mazur-Ulam theorem for normed gyrolinear spaces -- 4. Proofs of Theorem 3.5 and Corollary 3.6 -- 5. application -- References -- Sparse Hamburger moment multisequences -- 1. Introduction -- 2. Main Result -- 3. Completions -- 4. Some Counterexamples -- Acknowledgements -- References -- Polynomial representation of quantum entanglement -- 1. Introduction -- 2. Polynomial representation for a multipartite system and entanglement -- 3. Rational Functional Representation of Density Operators -- 4. Schmidt Decomposition in bipartite system -- 5. Examples -- 6. Discussion -- Acknowledgement -- References -- On span of small combination of slices points in Banach spaces -- 1. Introduction -- 2. Stability Result -- 3. ( , ) and ( , ) -- Acknowledgement -- References -- Surjective isometries on absolutely continuous vector valued function spaces -- 1. Introduction -- 2. Surjective isometries on ^{ }_{ } -- 3. Generalized bi-circular projections and bounded hermitian operators on ^{ }_{ } -- References -- Compactness, differentiability and similarity to isometry of composition semigroups -- 1. Introduction -- 2. Main results -- Acknowledgement -- References -- Weighted composition operators from Banach spaces of analytic functions into Bloch-type spaces -- 1. Introduction -- 2. _{ ,\f}: →\Bₐ for continuously contained in \B -- 3. The operator _{ ,\f}: ^{ }→\Bₐ for &gt -- 1 -- References -- A new proof of a Nordgren, Rosenthal and Wintrobe Theorem on universal operators -- 1. Introduction -- 2. A Toeplitz operator proof of Nordgren, Rosenthal and Wintrobe's Theorem -- References.

Wavelets and spectral triples for fractal representations of Cuntz algebras -- 1. Introduction -- 2. Cantor sets associated to directed graphs -- 3. The action of _{ } on ℒ²( _{ },ℍ) -- 4. Spectral triples and Laplacians for Cuntz algebras -- 5. Wavelets and eigenfunctions for _{ } -- 6. Spectral triples and Laplacians for the Cuntz algebra _{ }: the uneven weight case -- References -- The isometric equivalence problem -- 1. Introduction -- 2. Main Results -- 3. Recent Results: Hermitian and Surjective Isometries on Nakano Spaces -- Acknowledgment -- References -- Extension of isometries in generalized gyrovector spaces of the positive cones -- 1. Introduction -- 2. A positive cone as a GGV -- 3. The commutative case -- 4. -isometries between connected open sets -- References -- Generalized -circular projections on JB*-triples -- 1. Introduction -- 2. Results -- Acknowledgement -- References -- Hermitian operators on ¹_{ℋ} -- 1. Introduction -- 2. Hermitian operators on ¹_{ℋ} -- 3. Bounded Hermitian Operators on ¹_{ℋ} -- 4. Unbounded Hermitian Operators on ¹_{}ℋ -- 5. Acknowledgment -- References -- Kernels of adjoints of composition operators with rational symbols of degree two -- 1. Introduction -- 2. Background -- 3. Main Results -- 4. Conclusion -- References -- Surjective isometries on the Banach space of continuously differentiable functions -- 1. Introduction -- 2. Preliminaries -- 3. Construction of mappings -- 4. Proof of Theorem 1 -- 5. Acknowledgment -- References -- The arithmetic, geometric and harmonic means in operator algebras and transformations among them -- 1. Introduction -- 2. Results -- 3. Concluding remarks -- References -- On sign embeddings and narrow operators on ₂ -- 1. A brief overview of "weak" embeddings and narrow operators -- 2. New results -- References.

Into isometries that preserve finite dimensional structure of the range -- 1. Introduction -- 2. Main Results -- References -- Associating linear and nonlinear operators -- 1. Preliminaries -- 2. Developing the Measure -- 3. Associating a Linear Operator With -- References -- Normality properties of weighted composition operators on ² -- 1. Introduction -- 2. An overview of weak normality conditions -- 3. Self-adjoint weighted composition operators -- 4. Unitary weighted composition operators -- 5. Normal weighted composition operators -- 6. Quasinormal weighted composition operators -- 7. Hyponormal weighted composition operators -- 8. Subnormal weighted composition operators -- 9. Adjoints of weighted composition operators -- 10. Complex symmetric weighted composition operators -- 11. Conclusion -- 12. Acknowledgements -- References -- Back Cover.

This volume contains the proceedings of the Workshop on Problems and Recent Methods in Operator Theory, held at the University of Memphis, Memphis, TN, from October 15-16, 2015 and the AMS Special Session on Advances in Operator Theory and Applications, in Memory of James Jamison, held at the University of Memphis, Memphis, TN, from October 17-18, 2015. Operator theory is at the root of several branches of mathematics and offers a broad range of challenging and interesting research problems. It also provides powerful tools for the development of other areas of science including quantum theory, physics and mechanics. Isometries have applications in solid-state physics. Hermitian operators play an integral role in quantum mechanics very much due to their "nice" spectral properties. These powerful connections demonstrate the impact of operator theory in various branches of science. The articles in this volume address recent problems and research advances in operator theory. Highlighted topics include spectral, structural and geometric properties of special types of operators on Banach spaces, with emphasis on isometries, weighted composition operators, multi-circular projections on function spaces, as well as vector valued function spaces and spaces of analytic functions. This volume gives a succinct overview of state-of-the-art techniques from operator theory as well as applications to classical problems and long-standing open questions.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.