Modern approaches to the invariant-subspace problem / Isabelle Chalendar, Jonathan R. Partington.

Format:

Book

Author/Creator:

Chalendar, Isabelle, 1970-

Contributor:

Partington, Jonathan R. (Jonathan Richard), 1955-

Series:

Cambridge tracts in mathematics ; 188.

Cambridge tracts in mathematics

Language:

English

Subjects (All):

Invariant subspaces.

Hilbert space.

Physical Description:

xi, 285 pages : illustrations ; 24 cm.

Place of Publication:

Cambridge, UK ; New York : Cambridge University Press, 2011.

Summary:

"One of the major unsolved problems in operator theory is the fifty-year-old invariant subspace problem, which asks whether every bounded linear operator on a Hilbert space has a nontrivial closed invariant subspace. This book presents some of the major results in the area, including many that were derived within the past few years and cannot be found in other books. Beginning with a preliminary chapter containing the necessary pure mathematical background, the authors present a variety of powerful techniques, including the use of the operator-valued Poisson kernel, various forms of the functional calculus, Hardy spaces, fixed point theorems, minimal vectors, universal operators and moment sequences. The subject is presented at a level accessible to postgraduate students, as well as established researchers. It will be of particular interest to those who study linear operators and also to those who work in other areas of pure mathematics"-- Provided by publisher.

Contents:

The operator-valued Poisson kernel and its applications

Properties (An,m) and factorization of integrable functions

Polynomially bounded operators with rich spectrum

Beurling algebras

Applications of a fixed-point theorem

Minimal vectors

Universal operators

Moment sequences and binomial sums

Positive and strictly-singular operators.

Notes:

Includes bibliographical references and index.

ISBN:

9781107010512

1107010519

OCLC:

711048040

Online:

Cover image