Spectral Mapping Theorems
A Bluffer's Guide
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Beschreibung
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.
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
Autor*in
Robin Harte
Themen in »Spectral Mapping Theorems«
Gelfand Theory Joint Spectrum Muller Regularity Spectral Mapping Theorem in Several Variables
Stimmen zu »Spectral Mapping Theorems«
“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)
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