| Description |
1 online resource (299 pages). |
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text file |
| Series |
Cambridge Tracts in Mathematics, 188 ; v. 188
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Cambridge tracts in mathematics ; 188.
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| Contents |
Cover; Half-title; Title; Copyright; Contents; Preface; 1 Background; 1.1 Functional analysis; 1.1.1 Weak topology; 1.1.2 Hahn-Banach theorem; 1.1.3 Stone-Weierstrass theorem; 1.1.4 Banach-Steinhaus theorem; 1.1.5 Complex measures; 1.1.6 Riesz representation theorem; 1.1.7 Geometry of Banach spaces; 1.2 Operator theory; 1.2.1 Basic definitions and spectral properties; 1.2.2 Wold decomposition of an isometry; 1.2.3 Riesz -- Dunford functional calculus; 1.3 The Poisson kernel; 1.4 Hardy spaces; 1.4.1 Inner and outer functions; 1.4.2 Consequences of the inner -- outer factorization. |
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1.4.3 The theorems of Beurling and Wiener1.4.4 The disc algebra; 1.4.5 Reproducing kernels, Riesz bases and Carleson sequences; 1.4.6 Functions of bounded mean oscillation; 1.4.7 The Hilbert transform on the unit circle; 1.5 Number Theory; 2 The operator-valued Poisson kernel and its applications; 2.1 The operator-valued Poisson kernel; 2.2 The H8 functional calculus for absolutely continuous?-contractions; 2.3 H8 functional calculus in a complex Banach space; 2.4 Absolutely continuous elementary spectral measures; Exercises; Comments. |
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3 Properties (An, m) and factorization of integrable functions3.1 The basis of the S. Brown method; 3.1.1 The starting point; 3.1.2 The class A; 3.1.3 Classes An, m; 3.2 Factorization of log-integrable functions; 3.3 Applications in harmonic analysis; 3.4 Subnormal operators; 3.4.1 Borelian functional calculus for normal operators; 3.4.2 Invariant subspaces for subnormal operators; 3.5 Surjectivity of continuous bilinear mapping; 3.5.1 A sufficient condition for property (A?0); 3.5.2 A sufficient condition for property (A1,?0); Exercises; Comments. |
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4 Polynomially bounded operators with rich spectrum4.1 Apostol's theorem; 4.2 C2(T) functional calculus and the Colojoara-Foias theorem; 4.2.1 Operators with a C2(T) functional calculus; 4.2.2 The Colojoara-Foias theorem; 4.3 Zenger's theorem; 4.3.1 Zenger's theorem and a factorization result; 4.3.2 A stronger version of Zenger's theorem; 4.4 Carleson's interpolation theorem; 4.5 Approximation using Apostol sets; 4.5.1 Approximation of integrable non-negative functions; 4.5.2 Approximate eigenvalues; 4.6 Invariant subspace results; Exercises; Comments; 5 Beurling algebras. |
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5.1 Properties of Beurling algebras5.2 Theorems of Wermer and Atzmon; 5.3 Bishop operators; 5.3.1 Davie's functional calculus; 5.3.2 The point spectrum; 5.4 Rational Bishop operators; 5.4.1 Cyclic vectors; 5.4.2 The lattice of invariant subspaces; Exercises; Comments; 6 Applications of a fixed-point theorem; 6.1 Operators commuting with compact operators; 6.2 Essentially self-adjoint operators; 6.2.1 Preliminaries; 6.2.2 Application to invariant subspaces; Exercises; Comments; 7 Minimal vectors; 7.1 The basic definitions; 7.2 Minimal vectors in Hilbert space; 7.3 A general extremal problem. |
| Note |
7.3.1 Approximation in Hilbert spaces. |
| Summary |
Presents work on the invariant subspace problem, a major unsolved problem in operator theory. |
| Bibliography |
Includes bibliographical references and index. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Invariant subspaces.
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Invariant subspaces. |
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Hilbert space.
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Hilbert space. |
| Genre/Form |
Electronic books.
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| Added Author |
Partington, Jonathan R. (Jonathan Richard), 1955-
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| Other Form: |
Print version: Chalendar, Isabelle. Modern Approaches to the Invariant-Subspace Problem. Cambridge : Cambridge University Press, ©2011 9781107010512 |
| ISBN |
9781139117944 |
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1139117947 |
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1139115774 (electronic book) |
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9781139115773 (electronic book) |
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9781139128605 (electronic book) |
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1139128604 (electronic book) |
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9780511862434 (electronic book) |
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0511862431 (electronic book) |
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9781107010512 (hardback) |
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1107010519 (hardback) |
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