Functional Analysis An Introduction to Banach Space Theory

by Morrison, Terry J.

• ISBN13: 9780471372141
• ISBN10: 0471372145
• Edition: 1st
• Format: Hardcover
• Copyright: 2001-01-01
• Publisher: Wiley-Interscience

Summary

Functional analysis is one of the most active areas of mathematics at both the theoretical and applied levels, combining analytical, topological, and algebraic techniques in the study of topological vector spaces and operators between these spaces. This book offers a thorough introduction to functional analysis with a unique emphasis on Banach spaces.

Author Biography

TERRY J. MORRISON, PhD, is Associate Professor in the Department of Mathematics and Computer Science at Gustavus Adolphus College, St. Peter, Minnesota.

Table of Contents

Preface	ix
Introduction	1	(1)
Notation and Conventions	2	(2)
Products and the Product Topology	4	(4)
Finite-Dimensional Spaces and Riesz's Lemma	8	(3)
The Daniell Integral	11	(6)
Basic Definitions and Examples	17	(46)
Examples of Banach Spaces	17	(19)
Examples and Calculation of Dual Spaces	36	(27)
Basic Principles with Applications	63	(44)
The Hahn-Banach Theorem	64	(11)
The Banach-Steinhaus Theorem	75	(3)
The Open-Mapping and Closed-Graph Theorems	78	(4)
Applications of the Basic Principles	82	(25)
Weak Topologies and Applications	107	(48)
Convex Sets and Minkowski Functionals	108	(9)
Dual Systems and Weak Topologies	117	(7)
Convergence and Compactness in Weak Topologies	124	(20)
The Krein-Milman Theorem	144	(11)
Operators on Banach Spaces	155	(62)
Preliminary Facts and Linear Projections	156	(8)
Adjoint Operators	164	(6)
Weakly Compact Operators	170	(11)
Compact Operators	181	(5)
The Riesz-Schauder Theory	186	(15)
Strictly Singular and Strictly Cosingular Operators	201	(9)
Reflexivity and Factoring Weakly Compact Operators	210	(7)
Bases in Banach Spaces	217	(52)
Introductory Concepts	220	(12)
Bases in Some Special Spaces	232	(6)
Equivalent Bases and Complemented Subspaces	238	(8)
Basic Selection Principles	246	(23)
Sequences, Series, and a Little Geometry in Banach Spaces	269	(72)
Phillips' Lemma	270	(15)
Special Bases and Reflexivity in Banach Spaces	285	(18)
Unconditionally Converging and Dunford-Pettis Operators	303	(7)
Support Functionals and Convex Sets	310	(11)
Convexity and the Differentiability of Norms	321	(20)
Bibliography	341	(4)
Author/Name Index	345	(3)
Subject Index	348	(10)
Symbol Index	358