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Fundamentals of Functional Analysis

  • Douglas¬†Farenick

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Topology

    1. Front Matter
      Pages 1-1
    2. Douglas Farenick
      Pages 3-38
    3. Douglas Farenick
      Pages 39-74
  3. Measure Theory and Integration

    1. Front Matter
      Pages 75-75
    2. Douglas Farenick
      Pages 77-118
    3. Douglas Farenick
      Pages 119-161
  4. Banach Spaces

    1. Front Matter
      Pages 163-163
    2. Douglas Farenick
      Pages 165-213
    3. Douglas Farenick
      Pages 215-247
    4. Douglas Farenick
      Pages 249-268
  5. Operator Theory

    1. Front Matter
      Pages 269-269
    2. Douglas Farenick
      Pages 271-307
    3. Douglas Farenick
      Pages 309-328
    4. Douglas Farenick
      Pages 329-392
    5. Douglas Farenick
      Pages 393-441
  6. Back Matter
    Pages 443-451

About this book

Introduction

This book provides a unique path for graduate or advanced undergraduate students to begin studying the rich subject of functional analysis with fewer prerequisites than is normally required. The text begins with a self-contained and highly efficient introduction to topology and measure theory, which focuses on the essential notions required for the study of functional analysis, and which are often buried within full-length overviews of the subjects. This is particularly useful for those in applied mathematics, engineering, or physics who need to have a firm grasp of functional analysis, but not necessarily some of the more abstruse aspects of topology and measure theory normally encountered. The reader is assumed to only have knowledge of basic real analysis, complex analysis, and algebra.

The latter part of the text provides an outstanding treatment of Banach space theory and operator theory, covering topics not usually found together in other books on functional analysis. Written in a clear, concise manner, and equipped with a rich array of interesting and important exercises and examples, this book can be read for an independent study, used as a text for a two-semester course, or as a self-contained reference for the researcher. 

 

Keywords

measure theory operator theory Topological spaces Lebesgue intergral Banach spaces Banach space duality convexity theory Hilbert space Banach algebras operator algebras Choquet theory

Authors and affiliations

  • Douglas¬†Farenick
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of ReginaReginaCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-45633-1
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-45631-7
  • Online ISBN 978-3-319-45633-1
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site
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