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Look Inside Elements of Functional Analysis

Elements of Functional Analysis

2nd Edition


  • Date Published: January 1989
  • availability: Available
  • format: Paperback
  • isbn: 9780521358682

£ 45.99

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About the Authors
  • The second edition of this successful textbook, first published in 1970, retains the aims of the first, namely to provide a truly introductory course in functional analysis, but the opportunity has been taken to add more detail and worked examples. The main changes are complete revisons of the work on convex sets, metric and topological linear spaces, reflexivity and weak convergence. Additional material on the Weiner algebra of absolutely convergent Fourier series and on weak topologies is included. A final chapter includes elementary applications of functional analysis to differential and integral equations.

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    Product details

    • Edition: 2nd Edition
    • Date Published: January 1989
    • format: Paperback
    • isbn: 9780521358682
    • length: 256 pages
    • dimensions: 228 x 151 x 15 mm
    • weight: 0.35kg
    • availability: Available
  • Table of Contents

    Preface to the second edition
    Preface to the first edition
    Part I. Basic Set Theory and Analysis:
    1. Sets and functions
    2. Real and complex numbers
    3. Sequences of functions, continuity, differentiability
    4. Inequalities
    Part II. Metric and Topological Spaces:
    1. Metric and semimetric spaces
    2. Complete metric spaces
    3. Some metric and topological concepts
    4. Continuous functions on metric and topological spaces
    5. Compact sets
    6. Category and uniform boundedness
    Part III. Linear and Linear Metric Spaces:
    1. Linear spaces
    2. Subspaces, dimensionality, factorspaces, convex sets
    3. Metric linear spaces, topological linear spaces
    4. Basis
    Part IV. Normed Linear Spaces:
    1. Convergence and completeness
    2. Linear operators and functionals
    3. The Banach–Steinhaus theorem
    4. The open mapping and closed graph theorems
    5. The Hahn–Banach extension
    6. Weak topology and weak convergence
    Part V. 1. Algebras and Banach algebras
    2. Homomorphisms and isomorphisms
    3. The spectrum and the Gelfand–Mazaur theorem
    4. The Weiner algebra
    Part VI. Hilbert Space:
    1. Inner product and Hilbert spaces
    2. Orthonormal sets
    3. The dual space of a Hilbert space
    4. Symmetric and compact operators
    Part VII. Applications:
    1. Differential and integral problems
    2. The Sturm–Liouville problem
    3. Matrix transformations in sequence spaces

  • Author

    I. J. Maddox

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