Composition Operators on Function Spaces (North-holland Mathematical Library)

Very good book for Graduate students in Mathematics, especially those working on Functional Analysis. 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. 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 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 L P -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 Presents research on composition operators undertaken since 1970. The work deals with the operators on Lp-spaces. Topics covered include measurable dynamics, ergodic theory, classical mechanics, Markov processes and composition operators on functional Banach spaces (including Hardy spaces).