Introduction to the Analysis of Normed Linear Spaces

Front Cover
Cambridge University Press, Mar 13, 2000 - Mathematics - 280 pages
1 Review
This text is ideal for a basic course in functional analysis for senior undergraduate and beginning postgraduate students. John Giles provides insight into basic abstract analysis, which is now the contextual language of much modern mathematics. Although it is assumed that the student has familiarity with elementary real and complex analysis, linear algebra, and the analysis of metric spaces, the book does not assume a knowledge of integration theory or general topology. Its central theme concerns structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. Giles illustrates the general theory with a great variety of example spaces.
 

What people are saying - Write a review

User Review - Flag as inappropriate

basic properties normed lines space

Selected pages

Contents

NORMED LINEAR SPACE STRUCTURE AND EXAMPLES
1
Exercises
19
2 Classes of example spaces
24
Exercises
45
3 Orthonormal sets in inner product spaces
50
Exercises
64
SPACES OF CONTINUOUS LINEAR MAPPINGS
67
Exercises
86
13 Adjoint operators on Hilbert space
181
Exercises
193
14 Projection operators
196
Exercises
204
15 Compact operators
206
Exercises
214
Chapter VI SPECTRAL THEORY
217
Exercises
221

5 The shape of the dual
92
Exercises
110
THE EXISTENCE OF CONTINUOUS LINEAR FUNCTIONALS
113
Exercises
120
7 The natural embedding and reflexivity
122
Exercises
130
8 Subreflexivity
132
Exercises
138
Chapter IV THE FUNDAMENTAL MAPPING THEOREMS FOR BANACH SPACES
139
Exercises
150
10 The Open Mapping and Closed Graph Theorems
153
Exercises
158
11 The Uniform Boundedness Theorem
163
Exercises
169
Chapter V TYPES OF CONTINUOUS LINEAR MAPPINGS
171
Exercises
179
17 The spectrum of a continuous linear operator
222
Exercises
227
18 The spectrum of a compact operator
230
Exercises
235
19 The Spectral Theorem for compact normal operators on Hilbert space
237
Exercises
241
20 The Spectral Theorem for compact operators on Hilbert space
243
Exercises
250
APPENDIX
252
A2 Numerical equivalence
254
A3 Hamel basis
256
Historical notes
258
List of symbols
269
Index
272
Copyright

Common terms and phrases

Bibliographic information