Elementary Functional Analysis

By: Charles W Swartz

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Hardcover | 14 July 2009

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192 Pages

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22.86 x 15.24 x 1.27

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This text is an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis at the first-year graduate level. Prerequisite knowledge of general topology or Lebesgue integration is not required. The book explains the principles and applications of functional analysis and explores the development of the basic properties of normed linear, inner product spaces and continuous linear operators defined in these spaces. Though Lebesgue integral is not discussed, the book offers an in-depth knowledge on the numerous applications of the abstract results of functional analysis in differential and integral equations, Banach limits, harmonic analysis, summability and numerical integration. Also covered in the book are versions of the spectral theorem for compact, symmetric operators and continuous, self adjoint operators.

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Science Physics Algebra Booktopia Publisher Services World Scientific Publishing

Preface	p. v
Normed Linear and Banach Spaces	p. 1
Linear Operators	p. 9
Quotient Spaces	p. 21
Finite Dimensional Normed Spaces	p. 25
Inner Product and Hilbert Spaces	p. 29
The Hahn-Banach Theorem	p. 41
Applications of the Hahn-Banach Theorem to Normed Spaces	p. 47
The Uniform Boundedness Principle	p. 53
Weak Convergence	p. 61
The Open Mapping and Closed Graph Theorems	p. 69
Projections	p. 73
Schauder Basis	p. 77
Transpose and Adjoints of Continuous Linear Operators	p. 83
Compact Operators	p. 91
The Fredholm Alternative	p. 97
The Spectrum of an Operator	p. 103
Subdivisions of the Spectrum	p. 107
The Spectrum of a Compact Operator	p. 111
Symmetric Linear Operators	p. 115
The Spectral Theorem for Compact Symmetric Operators	p. 119
Symmetric Operators with Compact Inverse	p. 129
Bounded Self Adjoint Operators	p. 133
Orthogonal Projections	p. 141
Sesquilinear Functionals	p. 143
The Spectral Theorem for Bounded Self Adjoint Operators	p. 145
An Operational Calculus	p. 151
The Spectral Theorem for Normal Operators	p. 159
Functions of Bounded Variation	p. 163
The Riemann-Stieltjes Integral	p. 167
The Dual of C[a,b]	p. 169
The Baire Category Theorem	p. 173
References	p. 175
Index	p. 179
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Elementary Functional Analysis

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Hardcover

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How to return your order

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