A Primer, and Beyond, on Composition Operators on the Unit Disk (Hardcover) (ISBN-13: 9781009388894)

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.

Author: Pascal Lefèvre,Hervé Queffélec
ISBN-10: 1009388894
ISBN-13: 9781009388894
Publisher: Cambridge University Press
Language: English
Published: 06/11/2026
Pages: 602
Format: Hardcover
Weight: 2.13lbs
Size: 9.00h x 6.00w x 1.31d