Banach Algebras and Compact Operators - 1st Edition - ISBN: 9780444507501, 9780080528380

Banach Algebras and Compact Operators, Volume 2

1st Edition

Serial Editors: Corneliu Constantinescu
eBook ISBN: 9780080528380
Hardcover ISBN: 9780444507501
Imprint: North Holland
Published Date: 27th April 2001
Page Count: 620
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Table of Contents

Introduction.

  1. Banach Algebras.
    2.1 Algebras.
    2.1.1 General Results.
    2.1.2 Invertible Elements.
    2.1.3 The Spectrum.
    2.1.4 Standard Examples.
    2.1.5 Complexification of Algebras.
    Exercises.
    2.2 Normed Algebras.
    2.2.1 General Results.
    2.2.2 The Standard Examples.
    2.2.3 The Exponential Function and the Neumann Series.
    2.2.4 Invertible Elements of Unital Banach Algebras.
    2.2.5 The Theorems of Riesz and Gelfand.
    2.2.6 Poles of Resolvents.
    2.2.7 Modules.
    Exercises.
    2.3 Involutive Banach Algebras.
    2.3.1 Involutive Algebras.
    2.3.2 Involutive Banach Algebras.
    2.3.3 Sesquilinear Forms.
    2.3.4 Positive Linear Forms.
    2.3.5 The State Space.
    2.3.6 Involutive Modules.
    Exercises.
    2.4 Gelfand Algebras.
    2.4.1 The Gelfand Transform.
    2.4.2 Involutive Gelfand Algebras.
    2.4.3 Examples.
    2.4.4 Locally Compact Additive Groups.
    2.4.5 Examples.
    2.4.6 The Fourier Transform.
    Exercises.
  2. Compact Operators.
    3.1 The General Theory.
    3.1.1 General Results.
    3.1.2 Examples.
    3.1.3 Fredholm Operators.
    3.1.4 Point Spectrum.
    3.1.5 Spectrum of a Compact Operator.
    3.1.6 Integral Operators.
    Exercises.
    3.2 Linear Differential Equations.
    3.2.1 Boundary Value Problems for Differential Equations.
    3.2.2 Supplementary Results.
    3.2.3 Linear Partial Differential Equations.
    Exercises.
    Name Index. Subject Index. Symbol Index.

Details

No. of pages:
620
Language:
English
Copyright:
© North Holland 2001
Published:
Imprint:
North Holland
eBook ISBN:
9780080528380
Hardcover ISBN:
9780444507501

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About the Serial Editors

Corneliu Constantinescu Serial Editor

Affiliations and Expertise

Departement Mathematik, ETH Zürich, CH-8092 Zürich, Switzerland