Modern Approaches to the Invariant-Subspace Problem.
Presents work on the invariant subspace problem, a major unsolved problem in operator theory.
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Full Text (via Cambridge) |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge :
Cambridge University Press,
2011.
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| Series: | Cambridge Tracts in Mathematics, 188.
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| Subjects: |
MARC
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| 049 | |a GWRE | ||
| 100 | 1 | |a Chalendar, Isabelle. | |
| 245 | 1 | 0 | |a Modern Approaches to the Invariant-Subspace Problem. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2011. | ||
| 300 | |a 1 online resource (299 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Cambridge Tracts in Mathematics, 188 ; |v v. 188 | |
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 500 | |a 7.3.1 Approximation in Hilbert spaces. | ||
| 520 | |a Presents work on the invariant subspace problem, a major unsolved problem in operator theory. | ||
| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references and index. | ||
| 650 | 0 | |a Invariant subspaces. | |
| 650 | 0 | |a Hilbert space. | |
| 650 | 7 | |a Hilbert space. |2 fast |0 (OCoLC)fst00956785 | |
| 650 | 7 | |a Invariant subspaces. |2 fast |0 (OCoLC)fst00977981 | |
| 700 | 1 | |a Partington, Jonathan R. | |
| 776 | 0 | 8 | |i Print version: |a Chalendar, Isabelle. |t Modern Approaches to the Invariant-Subspace Problem. |d Cambridge : Cambridge University Press, ©2011 |z 9781107010512 |
| 830 | 0 | |a Cambridge Tracts in Mathematics, 188. | |
| 856 | 4 | 0 | |u https://colorado.idm.oclc.org/login?url=https://doi.org/10.1017/CBO9780511862434 |z Full Text (via Cambridge) |
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| 952 | f | f | |p Can circulate |a University of Colorado Boulder |b Online |c Online |d Online |h Library of Congress classification |i web |