Metrics, Norms, Inner Products, and Operator Theory

  • Christopher Heil

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Christopher Heil
    Pages 1-30
  3. Christopher Heil
    Pages 31-97
  4. Christopher Heil
    Pages 99-139
  5. Christopher Heil
    Pages 141-190
  6. Christopher Heil
    Pages 191-241
  7. Christopher Heil
    Pages 243-290
  8. Christopher Heil
    Pages 291-341
  9. Back Matter
    Pages 343-359

About this book


This text is a self-contained introduction to the three main families that we encounter in analysis – metric spaces, normed spaces, and inner product spaces – and to the operators that transform objects in one into objects in another.  With an emphasis on the fundamental properties defining the spaces, this book guides readers to a deeper understanding of analysis and an appreciation of the field as the “science of functions.”

Many important topics that are rarely presented in an accessible way to undergraduate students are included, such as unconditional convergence of series, Schauder bases for Banach spaces, the dual of ℓp topological isomorphisms, the Spectral Theorem, the Baire Category Theorem, and the Uniform Boundedness Principle.  The text is constructed in such a way that instructors have the option whether to include more advanced topics.

Written in an appealing and accessible style, Metrics, Norms, Inner Products, and Operator Theory is suitable for independent study or as the basis for an undergraduate-level course.  Instructors have several options for building a course around the text depending on the level and interests of their students.

Key features:

  • Aimed at students who have a basic knowledge of undergraduate real analysis.  All of the required background material is reviewed in the first chapter.
  • Suitable for undergraduate-level courses; no familiarity with measure theory is required.
  • Extensive exercises complement the text and provide opportunities for learning by doing.
  • A separate solutions manual is available for instructors via the Birkhäuser website (     
  • Unique text providing an undergraduate-level introduction to metrics, norms, inner products, and their associated operator theory.



Metric spaces Banach spaces Hilbert spaces Functional anlaysis Operator theory

Authors and affiliations

  • Christopher Heil
    • 1
  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

Bibliographic information

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