Universitext

Non-commutative Gelfand Theories

A Tool-kit for Operator Theorists and Numerical Analysts

Authors: Roch, Steffen, Santos, Pedro A., Silbermann, Bernd

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  • Provides an overview of 30 years of theoretical developments
  • Offers new results not yet published
  • Also includes a number of concrete applications in operator theory and numerical analysis
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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.

Reviews

From the reviews:

“This book consists of two parts, the first half of which can be thought of as a textbook suitable for a course on Banach algebras. … The book is remarkably well written, and puts together in a systematic manner the material that was only available before in the form of journal publications … . it is both accessible to graduate (and even advanced undergraduate) students and of interest to seasoned researchers working on various aspects of operator theory and numerical analysis.” (I. Spitkovsky, Mathematical Reviews, Issue 2012 e)

“The theme of this book is local principles, which are formulated in the language of Banach algebras and may be regarded as noncommutative Gelfand theories. … The book shall be useful for students and researchers working in operator theory, functional analysis and numerical analysis.” (Mohammad Sal Moslehian, Zentralblatt MATH, Vol. 1209, 2011)


Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $69.99
price for USA in USD (gross)
  • ISBN 978-0-85729-183-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA in USD
  • ISBN 978-0-85729-182-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Non-commutative Gelfand Theories
Book Subtitle
A Tool-kit for Operator Theorists and Numerical Analysts
Authors
Series Title
Universitext
Copyright
2011
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London Limited
eBook ISBN
978-0-85729-183-7
DOI
10.1007/978-0-85729-183-7
Softcover ISBN
978-0-85729-182-0
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XIV, 383
Number of Illustrations
12 b/w illustrations, 2 illustrations in colour
Topics