Nearly Invariant Subspaces and Their Applications

Erscheinungsjahr 2026
ISBN: 978-1-047-75154-4
Verlag: Cambridge University Press

Buch, Englisch, 144 Seiten

Reihe: London Mathematical Society Student Texts

This book offers a comprehensive introduction to nearly invariant subspaces, a subject of active contemporary research within functional analysis. Written for graduate students in mathematical analysis and suitable as a reference for experienced researchers, the book surveys the historical development of nearly invariant subspaces from their origins in the study of kernels of Toeplitz operators and invariant subspaces of shift operators. It presents recent advances, including applications to the invariant subspace problem, to truncated Toeplitz operators, and to strongly continuous semigroups of operators. Although mostly concerned with operators on Hardy spaces, the book includes a discussion of the subject in the context of Bergman and Dirichlet spaces too. The book begins with a chapter recalling basic results in analysis and function theory, and each chapter contains a selection of accessible exercises to supplement the text.

Autoren/Hrsg.

Partington, Jonathan R.

Inhaltsverzeichnis

Introduction; 1. Preliminaries; 2. The origins of the subject; 3. Toeplitz kernels; 4. Almost invariance; 5. Truncated Toeplitz operators; 6 Other function spaces; 7. Vectorial results; 8. Near invariance for semigroups; References; Author index; Subject index.

Über Autor(innen)

Partington, Jonathan R.
Jonathan Partington is an Emeritus professor of applied functional analysis at Leeds University. He was formerly an editor of the Journal of the London Mathematical Society and coordinator of the Leeds node of a European Research Training Network in Analysis and Operators. The author of over 200 papers in mathematics and engineering, he has also written the following books: An Introduction to Hankel Operators (1989), Interpolation, Identification, and Sampling (1997), Linear Operators and Linear Systems (2004), and Modern Approaches to the Invariant Subspace Problem (2011, with Isabelle Chalendar).