Non-commutative Gelfand Theories

A Tool-kit for Operator Theorists and Numerical Analysts

  • Steffen Roch
  • Pedro A. Santos
  • Bernd Silbermann

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Non-commutative Gelfand Theories

    1. Front Matter
      Pages 1-1
    2. Steffen Roch, Pedro A. Santos, Bernd Silbermann
      Pages 3-61
    3. Steffen Roch, Pedro A. Santos, Bernd Silbermann
      Pages 63-119
    4. Steffen Roch, Pedro A. Santos, Bernd Silbermann
      Pages 121-187
  3. Case Studies

    1. Front Matter
      Pages 189-189
    2. Steffen Roch, Pedro A. Santos, Bernd Silbermann
      Pages 191-258
    3. Steffen Roch, Pedro A. Santos, Bernd Silbermann
      Pages 259-316
    4. Steffen Roch, Pedro A. Santos, Bernd Silbermann
      Pages 317-367
  4. Back Matter
    Pages 369-383

About this book


Written as a hybrid between a research monograph and a textbook the first half of this book is concerned with basic concepts for the study of Banach algebras that, in a sense, are not too far from being commutative. Essentially, the algebra under consideration either has a sufficiently large center or is subject to a higher order commutator property (an algebra with a so-called polynomial identity or in short: Pl-algebra). In the second half of the book, a number of selected examples are used to demonstrate how this theory can be successfully applied to problems in operator theory and numerical analysis.

Distinguished by the consequent use of local principles (non-commutative Gelfand theories), PI-algebras, Mellin techniques and limit operator techniques, each one of the applications presented in chapters 4, 5 and 6 forms a theory that is up to modern standards and interesting in its own right.

Written in a way that can be worked through by the reader with fundamental knowledge of analysis, functional analysis and algebra, this book will be accessible to 4th year students of mathematics or physics whilst also being of interest to researchers in the areas of operator theory, numerical analysis, and the general theory of Banach algebras.


Algebras generated by projections Algebras generated by projections Banach algebras Banach algebras Fredholm property Fredholm property Local principles Local principles Non-commutative Gelfand theories Non-commutative Gelfand theories Numerical analysis Numerical analysis PI-algebras PI-algebras Singular integral operators Singular integral operators Stability Stability Wiener-Hopf operators Wiener-Hopf operators

Authors and affiliations

  • Steffen Roch
    • 1
  • Pedro A. Santos
    • 2
  • Bernd Silbermann
    • 3
  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Instituto Superior Técnico, Departamento de MatemáticaUniversidade Técnica de LisboaLisboaPortugal
  3. 3.Fakultät für MathematikTechnische Universität ChemnitzChemnitzGermany

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag London Limited 2011
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-85729-182-0
  • Online ISBN 978-0-85729-183-7
  • About this book
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