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Introduction to Operator Theory I

Elements of Functional Analysis

  • Arlen Brown
  • Carl Pearcy

Part of the Graduate Texts in Mathematics book series (GTM, volume 55)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Preliminaries

    1. Front Matter
      Pages 1-1
    2. Arlen Brown, Carl Pearcy
      Pages 3-11
    3. Arlen Brown, Carl Pearcy
      Pages 12-31
    4. Arlen Brown, Carl Pearcy
      Pages 32-55
    5. Arlen Brown, Carl Pearcy
      Pages 56-69
    6. Arlen Brown, Carl Pearcy
      Pages 70-101
    7. Arlen Brown, Carl Pearcy
      Pages 102-112
    8. Arlen Brown, Carl Pearcy
      Pages 113-135
    9. Arlen Brown, Carl Pearcy
      Pages 136-163
    10. Arlen Brown, Carl Pearcy
      Pages 164-192
    11. Arlen Brown, Carl Pearcy
      Pages 193-208
  3. Banach Spaces

    1. Front Matter
      Pages 209-209
    2. Arlen Brown, Carl Pearcy
      Pages 211-247
    3. Arlen Brown, Carl Pearcy
      Pages 248-271
    4. Arlen Brown, Carl Pearcy
      Pages 272-282
    5. Arlen Brown, Carl Pearcy
      Pages 283-310
    6. Arlen Brown, Carl Pearcy
      Pages 311-336
    7. Arlen Brown, Carl Pearcy
      Pages 337-363
    8. Arlen Brown, Carl Pearcy
      Pages 364-405
    9. Arlen Brown, Carl Pearcy
      Pages 406-427
    10. Arlen Brown, Carl Pearcy
      Pages 428-449
  4. Back Matter
    Pages 451-476

About this book

Introduction

This book was written expressly to serve as a textbook for a one- or two-semester introductory graduate course in functional analysis. Its (soon to be published) companion volume, Operators on Hilbert Space, is in­ tended to be used as a textbook for a subsequent course in operator theory. In writing these books we have naturally been concerned with the level of preparation of the potential reader, and, roughly speaking, we suppose him to be familiar with the approximate equivalent of a one-semester course in each of the following areas: linear algebra, general topology, complex analysis, and measure theory. Experience has taught us, however, that such a sequence of courses inevitably fails to treat certain topics that are important in the study of functional analysis and operator theory. For example, tensor products are frequently not discussed in a first course in linear algebra. Likewise for the topics of convergence of nets and the Baire category theorem in a course in topology, and the connections between measure and topology in a course in measure theory. For this reason we have chosen to devote the first ten chapters of this volume (entitled Part I) to topics of a preliminary nature. In other words, Part I summarizes in considerable detail what a student should (and eventually must) know in order to study functional analysis and operator theory successfully.

Keywords

Funktionalanalysis Hilbert space Operator Operator theory functional analysis

Authors and affiliations

  • Arlen Brown
    • 1
  • Carl Pearcy
    • 2
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-9926-4
  • Copyright Information Springer-Verlag New York 1977
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-9928-8
  • Online ISBN 978-1-4612-9926-4
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site