内容简介

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作品目录

Preface

Introduction

Contents of Other Volumes

I: PRELIMINARIES

1. Sets and functions

2. Metric and normed linear spaces

Appendix Lira sup and lim inf

3. The Lebesgue integral

4. Abstract measure theory

5. Two conrergence arguments

6. Equicontinuity

Notes

Problems

II: HILBERT SPACES

1. The geometry of Hilbert space

2. The Riesz lemma

3. Orthonormal bases

4. Tensor products of Hilbert spaces

5. Ergodic theory: an introduction

Notes

Problems

III:　BANACH　SPACES

1. Definition　and　examples

2. Duals　and　double　duals

3. The　Hahn-Banach　theorem

4. Operations　on　Banach　spaces

5. The　Baire category　theorem　and　its　consequences

Notes

Problems

IV:　TOPOLOGICAL　SPACES

1. General　notions

2. Nets　and　Convergence

3. Compactness

Appendix The　Stone-Weierstrass　theorem

4. Measure　theory　on Compact　spaces

5. Weak　topologies　on　Banach　spaces

Appendix Weak　and　strong　measurability

Notes

Problems

V: LOCALLY ONVEX　SPACES

1. General　properties

2. Frdchet　spaces

3. Functions　of　rapid　decease　and　the　tempered　distributions

Appendix The　N-representation　for　and

4. Inductive　limits:　generalized　functions　and　weak　solutions　of partial　differential　equations

5. Fixed　point　theorems

6. Applications　of　fixed　point　theorems

7. Topologies　on　locally　convex　spaces:　duality　theory　and　the strong　dual　topology

Appendix Polars　and　the　Mackey-Arens　theorem

Notes

Problems

VI: BOUNDED　OPERATORS

VII: THE　SPECTRAL　THEOREM

VIII: UNBOUNDED　OPERATORS

THE　FOURIER　TRANSFORM

SUPPLEMENTARY　MATERIAL

List　of　Symbols