Composition Operators on Function Spaces (eBook)

J.S. Manhas, R.K. Singh (Autoren)

eBook Download: PDF

1993 | 1. Auflage
314 Seiten
Elsevier Science (Verlag)
9780080872902 (ISBN)

Infos

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 L^p-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.

Inhalt

Front Cover 1
Composition Operators on Function Spaces 4
Copyright Page 5
CONTENTS 10
PREFACE 6
Chapter I. INTRODUCTION 12
1.1 Definitions and Historical Background 12
1.2 LP–Spaces 15
1.3 Functional Banach Spaces of Functions 17
1.4 Locally Convex Function Spaces 21
Chapter II. COMPOSITION OPERATORS ON LP–SPACES 28
2.1 Definitions, Characterizations and Examples 28
2.2 Invertible Composition Operators 36
2.3 Compact Composition Operators 42
2.4 Normality of Composition Operators 47
2.5 Weighted Composition Operators 62
Chapter III. COMPOSITION OPERATORS ON FUNCTIONAL BANACH SPACES 70
3.1 General Characterizations 70
3.2 Composition Operators on Spaces Hp(D), Hp (Dn) and Hp(Dn) 73
3.3 Composition Operators on Hp(P+) 89
3.4 Composition Operators on lp –Spaces 95
Chapter IV. COMPOSITION OPERATORS ON THE WEIGHTED LOCALLY CONVEX FUNCTION SPACES 104
4.1 Introduction, Characterization and Classical Results 104
4.2 Composition Operators on the Weighted Locally Convex Function Spaces 109
4.3 Invertible and Compact Composition Operators on Weighted Function Spaces 140
4.4 Weighted Composition Operators on Weighted Function Spaces 149
Chapter V. SOME APPLICATIONS OF COMPOSITION OPERATORS 176
5.1 Isometries and Composition Operators 176
5.2 Ergodic Theory and Composition Operators 202
5.3 Dynamical Systems and Composition Operators 225
5.4 Homomorphisms and Composition Operators 270
REFERENCES 284
SYMBOL INDEX 314
SUBJECT INDEX 318

Produkt-Details

• Erscheint lt. Verlag: 3.11.1993
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Technik
• ISBN-13: 9780080872902 / 9780080872902