A Course in Functional Analysis (Graduate texts in mathematics) 1st edition, 1985
by John B Conway
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Number Of Pages: 404
Publication Date: 1985-12-31
Sales Rank: 3733949
ISBN / ASIN: 3540960422
EAN: 9783540960423
Binding: Paperback
Manufacturer: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Studio: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Alternate ISBN
* Unknown Binding: 404 pages
* Publisher: Springer-Verlag (1985)
* Language: English
* ISBN-10: 0387960422
* ISBN-13: 978-0387960425
Co ntents
Preface
CHAPTER I
Hilbert Spaces
§1. Elementary Properties and Examples
§2. Orthogonality
§3. The Riesz Representation Theorem
$4. Orthonormal Sets of Vectors and Bases
§5. Isomorphic Hilbert Spaces and the Fourier Transform
for the Circle
96. The Direct Sum of Hilbert Spaces
CHAPTER II
Operators on Hilbert Space
§1. Elementary Properties and Examples
92. The Adjoint of an Operator
§3. Projections and Idempotents; Invariant and Reducing
Subspaces
4. Compact Operators
§5.* The Diagonalization of Compact Self-Adjoint Operators
§6.* An Application: Sturrr-Liouville Systems
§7.* The Spectral Theorem and Functional Calculus for
Compact Normal Operators
§8.* Unitary Equivalence for Compact Normal Operators
CHAPTER III
Banach Spaces
§1. Elementary Properties and Examples
$2. Linear Operators on Normed Spaces
5. Stone s Theorem
$6. The Fourier Transform and Differentiation
$7. Moments
CHAPTER XI
Predholm Theory
$1. The Spectrum Revisited
§2. The Essential Spectrum and Semi-Fredholm Operators
§3. The Fredholm Index
4. The Components of
§5. A Finer Analysis of the Spectrum
APPENDIX A
Preliminaries
§1. Linear Algebra
§2. Topology
APPENDIX B
The Dual of LP(t0
APPENDIX C
The Dual of Co(X)
Bibliography
List of Symbols
Index
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