Rate this book

FUNCTIONAL ANALYSIS

Thamarai Selvi

Rate this book

Contentsi
1Normed Spaces3
Basic Definitions3
Subspaces and Quotient Spaces4
Completions6
Direct Sums7
Initial Topologies9
Nets10
Exercises 114
2Linear Operators17
Preliminaries17
Completeness of B(X, Y )18
Extension of Linear Operators18
The Baire Category Theorem19
The Open-Mapping Theorem21
Exercises 222
The Closed-Graph Theorem26
The Principle of Uniform Boundedness27
The Strong Operator Topology27
Exercises 328
3Dual Spaces31
Initial Definitions31
The Weak Topology31
Zorn’s Lemma32
The Hahn-Banach Theorem32
The Weak Operator Topology36
Adjoint Operators36
The Weak* Topology37
Exercises 437
Tychonov’s Theorem39
iiContents
The Banach-Alaoglu Theorem40
Topological Vector Spaces41
The Krein-Milman Theorem45
Exercises 547
4Normed Algebras53
Quotient Algebras54
Unitization55
Approximate Identities56
Completion57
5Invertibility59
The Spectrum and Resolvent60
The Gelfand-Mazur Theorem61
The Spectral-Radius Formula61
Exercises 663
6Characters and Maximal Ideals65
Characters and the Spectrum66
The Gelfand Topology67
The Representation Theorem68
Examples68
Exercises 772
ATychonov via Nets75
Exercises A78
Solutions to Exercises79
Exercises 179
Exercises 283
Exercises 388
Exercises 492
Exercises 597
Exercises 6105
Exercises 7109
Exercises A116
Bibliography117
Index119

332 pages, Kindle Edition

Published December 24, 2020

1 person want to read