Functional analysis : an introduction to Banach space theory / Terry J. Morrison.

Format:

Book

Author/Creator:

Morrison, Terry J., 1947-

Series:

Pure and applied mathematics (John Wiley & Sons : Unnumbered)

Pure and applied mathematics

Language:

English

Subjects (All):

Functional analysis.

Physical Description:

xi, 359 pages : illustrations ; 25 cm.

Place of Publication:

New York : J. Wiley, [2001]

Contents:

Products and the Product Topology 4

Finite-Dimensional Spaces and Riesz's Lemma 8

The Daniell Integral 11

1. Basic Definitions and Examples 17

1.1 Examples of Banach Spaces 17

1.2 Examples and Calculation of Dual Spaces 36

2. Basic Principles with Applications 63

2.1 The Hahn-Banach Theorem 64

2.2 The Banach-Steinhaus Theorem 75

2.3 The Open-Mapping and Closed-Graph Theorems 78

2.4 Applications of the Basic Principles 82

3. Weak Topologies and Applications 107

3.1 Convex Sets and Minkowski Functionals 108

3.2 Dual Systems and Weak Topologies 117

3.3 Convergence and Compactness in Weak Topologies 124

3.4 The Krein-Milman Theorem 144

4. Operators on Banach Spaces 155

4.1 Preliminary Facts and Linear Projections 156

4.2 Adjoint Operators 164

4.3 Weakly Compact Operators 170

4.4 Compact Operators 181

4.5 The Riesz-Schauder Theory 186

4.6 Strictly Singular and Strictly Cosingular Operators 201

4.7 Reflexivity and Factoring Weakly Compact Operators 210

5. Bases in Banach Spaces 217

5.1 Introductory Concepts 220

5.2 Bases in Some Special Spaces 232

5.3 Equivalent Bases and Complemented Subspaces 238

5.4 Basic Selection Principles 246

6. Sequences, Series, and a Little Geometry in Banach Spaces 269

6.1 Phillips' Lemma 270

6.2 Special Bases and Reflexivity in Banach Spaces 285

6.3 Unconditionally Converging and Dunford-Pettis Operators 303

6.4 Support Functionals and Convex Sets 310

6.5 Convexity and the Differentiability of Norms 321.

Notes:

Published simultaneously in Canada.

"A Wiley-Interscience Publication."

Includes bibliographical references (pages 341-344) and indexes.

ISBN:

0471372145

OCLC:

43729125