"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." Read more...
Abstract:
The authors survey the state of current research on the invariant subspace problem for linear operators, a major unsolved problem in mathematics that has inspired much research in the past fifty years. The subject is presented at a level suitable for postgraduate students and established researchers in mathematics. Read more...
Author(s): Chalendar, Isabelle; Partington, Jonathan Richard
Series: Cambridge tracts in mathematics 188
Publisher: Cambridge University Press
Year: 2011
Language: English
Pages: 285
City: New York, Cambridge (UK)
Tags: Invariant subspaces.;Hilbert space.;Sous-espaces invariants.;Hilbert, Espace de.;Hilbert, Espaces de.
Content: Introduction
1. Background
2. The operator-valued Poisson kernel and its applications
3. Properties (An,m) and factorization of integrable functions
4. Polynomially bounded operators with rich spectrum
5. Beurling algebras
6. Applications of a fixed-point theorem
7. Minimal vectors
8. Universal operators
9. Moment sequences and binomial sums
10. Positive and strictly-singular operators
Bibliography
Index.
