Modern Approaches to the Invariant-Subspace Problem.

Presents work on the invariant subspace problem, a major unsolved problem in operator theory.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Chalendar, Isabelle
Otros Autores: Partington, Jonathan R.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 2011.
Colección:Cambridge Tracts in Mathematics, 188.
Temas:
Invariant subspaces.
Hilbert space.
Sous-espaces invariants.
Espace de Hilbert.
MATHEMATICS > Functional Analysis.
Hilbert space
Invariant subspaces
Acceso en línea:Texto completo

MARC

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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. 
590 |a eBooks on EBSCOhost  |b EBSCO eBook Subscription Academic Collection - Worldwide 
650 0 |a Invariant subspaces. 
650 0 |a Hilbert space. 
650 6 |a Sous-espaces invariants. 
650 6 |a Espace de Hilbert. 
650 7 |a MATHEMATICS  |x Functional Analysis.  |2 bisacsh 
650 7 |a Hilbert space  |2 fast 
650 7 |a Invariant subspaces  |2 fast 
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. 
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