Composition Operators on Function Spaces

R.K. Singh and J.S. Manhas (Eds.)0444815937, 9780444815934, 9780080872902

This volume of the “Mathematics Studies” series 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, postgraduate students of mathematics and statistics, as well as to physicists and engineers.

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Table of contents :
Content:
Edited by
Pages ii-iii

Copyright page
Page iv

Preface
Pages v-viii
R.K. Singh

Chapter I Introduction
Pages 1-15

Chapter II Composition Operators on LP-Spaces
Pages 17-58

Chapter III Composition Operators on Functional Banach Spaces
Pages 59-91

Chapter IV Composition Operators on the Weighted Locally Convex Function Spaces
Pages 93-163

Chapter V Some Applications of Composition Operators
Pages 165-272

References
Pages 273-301

Symbol Index
Pages 303-305

Subject Index
Pages 307-315