Book 2014

Functional Analysis

An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras

Authors:

ISBN: 978-3-319-06727-8 (Print) 978-3-319-06728-5 (Online)

Table of contents (15 chapters)

  1. Front Matter

    Pages i-xi

  2. No Access

    Chapter

    Pages 1-10

    Introduction

  3. Metric Spaces

    1. Front Matter

      Pages 11-11

    2. No Access

      Chapter

      Pages 13-26

      Distance

    3. No Access

      Chapter

      Pages 27-36

      Convergence and Continuity

    4. No Access

      Chapter

      Pages 37-55

      Completeness and Separability

    5. No Access

      Chapter

      Pages 57-64

      Connectedness

    6. No Access

      Chapter

      Pages 65-85

      Compactness

  4. Banach and Hilbert Spaces

    1. Front Matter

      Pages 87-87

    2. No Access

      Chapter

      Pages 89-114

      Normed Spaces

    3. No Access

      Chapter

      Pages 115-138

      Continuous Linear Maps

    4. No Access

      Chapter

      Pages 139-169

      Main Examples

    5. No Access

      Chapter

      Pages 171-219

      Hilbert Spaces

    6. No Access

      Chapter

      Pages 221-256

      Banach Spaces

    7. No Access

      Chapter

      Pages 257-274

      Differentiation and Integration

  5. Banach Algebras

    1. Front Matter

      Pages 275-275

    2. No Access

      Chapter

      Pages 277-305

      Banach Algebras

    3. No Access

      Chapter

      Pages 307-343

      Spectral Theory

    4. No Access

      Chapter

      Pages 345-392

      \(C^*\) -Algebras

  6. Back Matter

    Pages 393-420