# Composition Operators on Function Spaces

This volume of the Mathematics Studies presents work done on composition operators during the last 25 years. Composition operators form a simple but interesting class of operators having interactions with different branches of mathematics and mathematical physics.

After an introduction, the book deals with these operators on Lp-spaces. This study is useful in measurable dynamics, ergodic theory, classical mechanics and Markov process. The composition operators on functional Banach spaces (including Hardy spaces) are studied in chapter III. This chapter makes contact with the theory of analytic functions of complex variables. Chapter IV presents a study of these operators on locally convex spaces of continuous functions making contact with topological dynamics. In the last chapter of the book some applications of composition operators in isometries, ergodic theory and dynamical systems are presented. An interesting interplay of algebra, topology, and analysis is displayed.

This comprehensive and up-to-date study of composition operators on different function spaces should appeal to research workers in functional analysis and operator theory, post-graduate students of mathematics and statistics, as well as to physicists and engineers.

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Published: November 1993

Imprint: North-holland

ISBN: 978-0-444-81593-4

## Contents

• Preface. Introduction. Definitions and historical background. Lp-spaces. Functional Banach spaces of functions. Locally convex function spaces. Composition Operators on Lp-spaces. Definitions, characterizations and examples. Invertible composition operators. Compact composition operators. Normality of composition operators. Weighted composition operators. Composition Operators on Functional Banach Spaces. General characterizations. Composition operators on spaces Hp(D), Hp(Dn) and Hp(Dn). Composition operators on Hp(P+). Composition operators on lp-spaces. Composition Operators on the Weighted Locally Convex Function Spaces. Introduction, characterization and classical results. Composition operators on the weighted locally convex function spaces. Invertible and compact composition operators on weighted function spaces. Some Applications of Composition Operators. Isometries and composition operators. Ergodic theory and composition operators. Dynamical systems and composition operators. Homomorphisms and composition operators. References. Symbol Index. Subject Index.