A primer, and beyond, on composition operators on the unit disk / Pascal Lefèvre, Hervé Queffélec

Format:

Book

Author/Creator:

Lefèvre, Pascal, 1969- author.

Queffélec, Hervé, author.

Series:

New mathematical monographs ; 55.

New mathematical monographs ; 55

Language:

English

Subjects (All):

Banach spaces.

Orlicz spaces.

Physical Description:

1 online resource

Place of Publication:

Cambridge : Cambridge University Press, 2026

Summary:

"This is a contemporary treatment of composition operators on Banach spaces of analytic functions in one complex variable. It provides a step-by-step introduction, starting with a review (including full proofs) of the key tools needed, and building the theory with a focus on Hardy and Bergman spaces. Several proofs of operator boundedness (Littlewood's principle) are given, and the authors discuss approaches to compactness issues and essential norm estimates (Shapiro's theorem) using different tools such as Carleson measures and Nevanlinna counting functions. Membership of composition operators in various ideal classes (Schatten classes for instance) and their singular numbers are studied. This framework is extended to Hardy-Orlicz and Bergman-Orlicz spaces and finally, weighted Hardy spaces are introduced, with a full characterization of those weights for which all composition operators are bounded. This will be a valuable resource for researchers and graduate students working in functional analysis, operator theory, or complex analysis"-- Cambridge Core

Contents:

Introduction : Toolbox

Boundedness of Composition Operators

A First Contact with Compactness Issues

Fundamental Examples

Carleson Embedding Point of View

Compactness via Nevanlinna Counting Functions and Essential Norms

Carleson versus Nevanlinna

Spectrum

Schatten Classes for Composition Operators

Approximation Numbers on Hardy and Bergman Spaces

Composition Operators on Hardy-Orlicz and Bergman-Orlicz Spacespp

Composition Operators on Weighted Hardy Spaces

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (Cambridge Core, viewed May 19, 2026)

Other Format:

Print version: Lefèvre, Pascal, 1969- Primer, and beyond, on composition operators on the unit disk

ISBN:

9781009388917

1009388916

OCLC:

1582437896

Publisher Number:

CIPO000359497

Access Restriction:

Restricted for use by site license