Operator theory in function spaces / Kehe Zhu

Auteur principal : Zhu, Kehe, 1961-, AuteurType de document : MonographieCollection : Mathematical surveys and monographs, 138Langue : anglais.Pays: Etats Unis.Mention d'édition: 2nd editionÉditeur : Providence : American Mathematical Society, 2007Description : 1 vol. (XVI-348 p.) ; 26 cmISBN: 9780821839652.ISSN: 0885-4653.Bibliographie : Bibliogr. p. 325-344. Index.Sujet MSC : 47-02, Research exposition (monographs, survey articles) pertaining to operator theory
47B38, Operator theory - Special classes of linear operators, Linear operators on function spaces (general)
47B33, Operator theory - Special classes of linear operators, Linear composition operators
47B35, Operator theory - Special classes of linear operators, Toeplitz operators, Hankel operators, Wiener-Hopf operators
47B10, Operator theory - Special classes of linear operators, Linear operators belonging to operator ideals
En-ligne : Zentralblatt | MathScinet | AMS Item type: Monographie
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Bibliogr. p. 325-344. Index

This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes.

Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study.

The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. (source : AMS)

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