Overview
- Useful as a supplement to any of the more orthodox texts in functional analysis and operator theory
- Provides an easily-grasped overview of the spectral mapping theorem, for polynomials in one, several and many variables, and their relationship with the Gelfand theory of Banach algebras
- Written in deliberately conversational style, these notes function as an extended seminar or workshop in this kind of spectral theory
- Includes supplementary material: sn.pub/extras
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Written by an author who was at the forefront of developments in multi-variable spectral theory during the seventies and the eighties, this guide sets out to describe in detail the spectral mapping theorem in one, several and many variables. The basic algebraic systems – semigroups, rings and linear algebras – are summarised, and then topological-algebraic systems, including Banach algebras, to set up the basic language of algebra and analysis.
Spectral Mapping Theorems is written in an easy-to-read and engaging manner and will be useful for both the beginner and expert. It will be of great importance to researchers and postgraduates studying spectral theory.
Reviews
“This short book introduces the reader to all algebraic, topological and operator theory … . The spectrum is defined and explained in detail, including the point, approximate point and essential spectrum … . the book is an excellent read if one aims to learn the abstract theory of spectral mapping theorems in one, several and many variables.” (Milena Stanislavova, Mathematical Reviews, October, 2015)
“Offering a fresh perspective even for experts, Harte (Trinity College, Ireland) emphasizes concepts of spectra generalized beyond single operators, so they are attached to finite sequences and even structured infinite families of operators. … Summing Up: Recommended. Upper-division undergraduates and above.” (D. V. Feldman, Choice, Vol. 52 (7), March, 2015)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Spectral Mapping Theorems
Book Subtitle: A Bluffer's Guide
Authors: Robin Harte
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-05648-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Robin Harte 2014
eBook ISBN: 978-3-319-05648-7Published: 29 April 2014
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: XIV, 120
Number of Illustrations: 1 b/w illustrations
Topics: Operator Theory