Handbook of analytic operator theory
Publisher’s description: This handbook concerns the subject of holomorphic function spaces and operators acting on them. Topics include Bergman spaces, Hardy spaces, Besov/Sobolev spaces, Fock spaces, and the space of Dirichlet series. Operators discussed in the book include Toeplitz operators, Hank...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Boca Raton, London, New York
CRC Press, Taylor & Francis Group
2019
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| Schriftenreihe: | Chapman & Hall/CRC handbooks in mathematics series
A Chapman & Hall book |
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| Online Zugang: | Inhaltsverzeichnis Inhaltstext Beschreibung & Leseprobe |
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Tag hinzufügen | Zusammenfassung: | Publisher’s description: This handbook concerns the subject of holomorphic function spaces and operators acting on them. Topics include Bergman spaces, Hardy spaces, Besov/Sobolev spaces, Fock spaces, and the space of Dirichlet series. Operators discussed in the book include Toeplitz operators, Hankel operators, composition operators, and Cowen-Douglas class operators. Cover; 1 Fock Space, the Heisenberg Group, Heat Flow, and Toeplitz Operators; 1.1 Introduction; 1.2 Toeplitz operators and the Heisenberg group; 1.3 Toeplitz operators and the Bargmann transform; 1.4 Limit behavior of ║T(t)f║t and ║H(t)f║t as t → 0; 1.5 Examples; References; 2: Two-Variable Weighted Shifts in Multivariable Operator Theory; 2.1 Introduction; 2.2 2-variable weighted shifts; 2.3 The lifting problem for commuting subnormals; 2.4 Hyponormality, 2-hyponormality and subnormality for 2-variable weighted shifts; 2.5 Existence of nonsubnormal hyponormal 2-variable weighted shifts; 2.6 Propagation in the 2-variable hyponormal case; 2.7 A measure-theoretic necessary (but not sufficient!) condition for the existence of a lifting; 2.8 Reconstruction of the Berger measure for 2-variable weighted shifts whose core is of tensor form; 2.9 The subnormal completion problem for 2-variable weighted shifts; 2.10 Spectral picture of hyponormal 2-variable weighted shifts; 2.11 A bridge between 2-variable weighted shifts and shifts on directed trees; 2.12 The spherical Aluthge transform; References 3: Commutants, Reducing Subspaces, and von Neumann Algebras; 3.1 Introduction; 3.2 Commutants and reducing subspaces for multiplication operators on the Hardy space H2(D); 3.3 The case of the Bergman space L2a(D); 3.4 The case of Bergman space over a polygon; 3.5 The case of the Bergman space over high dimensional domains; 3.6 Further questions; References; 4: Operators in the Cowen-Douglas Class and Related Topics; 4.1 Introduction; 4.2 Some future directions and further thoughts; References; 5: Toeplitz Operators and Toeplitz C*-Algebras; 5.1 Introduction 5.2 Toeplitz operators on Hilbert spaces of multi-variable holomorphic functions; 5.3 Strongly pseudoconvex domains; 5.4 Symmetric domains and Jordan triples; 5.5 Holomorphic function spaces on symmetric domains; 5.6 Toeplitz C*-algebras on symmetric domains; 5.7 Hilbert quotient modules and Kepler varieties; 5.8 Toeplitz operators on Reinhardt domains; References; 6: Möbius Invariant Zp and ZK Spaces; 6.1 Introduction; 6.2 Background; 6.3 Basic properties of Zp spaces; 6.4 Carleson measures; 6.5 The boundary value characterizations; 6.6 ZK spaces; 6.7 K-Carleson measures 6.8 Boundary ZK spaces; 6.9 Composition operators on Zp and ZK spaces; References; 7: Analytical Aspects of the Drury-Arveson Space; 7.1 Introduction; 7.2 von Neumann inequality for row contractions; 7.3 The multipliers; 7.4 A family of reproducing-kernel Hilbert spaces; 7.5 Essential normality; 7.6 Expanding on Drury's idea; 7.7 Closure of the polynomials; References; 8: A Brief Survey of Operator Theory in H2(D2); 8.1 Introduction; 8.2 Background; 8.3 Nagy-Foias theory in H2(D2); 8.4 Commutators; 8.5 Two-variable Jordan block; 8.6 Fredholmness of the pairs (R1,R2) and (S1,S2) This handbook concerns the subject of holomorphic function spaces and operators acting on them. Topics include Bergman spaces, Hardy spaces, Besov/Sobolev spaces, Fock spaces, and the space of Dirichlet series. Operators discussed in the book include Toeplitz operators, Hankel operators, composition operators, and Cowen-Douglas class operators |
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| Beschreibung: | Enthält bibliographische Hinweise und Index |
| Beschreibung: | ix, 359 Seiten Diagramme |
| ISBN: | 9781138486416 978-1-138-48641-6 1138486418 1-138-48641-8 |