Spectral mapping theorems
Author | : R. E. Harte |
Publisher | : |
Total Pages | : |
Release | : 1972 |
Genre | : |
ISBN | : |
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Author | : R. E. Harte |
Publisher | : |
Total Pages | : |
Release | : 1972 |
Genre | : |
ISBN | : |
Author | : Robin Harte |
Publisher | : Springer Nature |
Total Pages | : 193 |
Release | : 2023-04-03 |
Genre | : Mathematics |
ISBN | : 3031139178 |
Written by an author who was at the forefront of developments in multivariable spectral theory during the seventies and the eighties, this book describes the spectral mapping theorem in various settings. In this second edition, the Bluffer's Guide has been revised and expanded, whilst preserving the engaging style of the first. Starting with a summary of the basic algebraic systems – semigroups, rings and linear algebras – the book quickly turns to topological-algebraic systems, including Banach algebras, to set up the basic language of algebra and analysis. Key aspects of spectral theory are covered, in one and several variables. Finally the case of an arbitrary set of variables is discussed. Spectral Mapping Theorems is an accessible and easy-to-read guide, providing a convenient overview of the topic to both students and researchers. From the reviews of the first edition "I certainly plan to add it to my own mathematical library" — Anthony Wickstead in the Irish Mathematical Society Bulletin "An excellent read" — Milena Stanislavova in the Mathematical Reviews "[Offers] a fresh perspective even for experts [...] Recommended" — David Feldman in Choice
Author | : Robin Harte |
Publisher | : Springer |
Total Pages | : 132 |
Release | : 2014-04-29 |
Genre | : Mathematics |
ISBN | : 3319056484 |
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.
Author | : Mihai Putinar |
Publisher | : |
Total Pages | : 8 |
Release | : 1980 |
Genre | : |
ISBN | : |
Author | : James Joseph Dudziak |
Publisher | : |
Total Pages | : 204 |
Release | : 1981 |
Genre | : Subnormal operators |
ISBN | : |
Author | : Yasuhiko Ikebe |
Publisher | : |
Total Pages | : 17 |
Release | : 1984 |
Genre | : |
ISBN | : |
Author | : Mark Lichtner |
Publisher | : |
Total Pages | : 13 |
Release | : 2006 |
Genre | : |
ISBN | : |
Author | : Colin R. Day |
Publisher | : |
Total Pages | : 68 |
Release | : 1992 |
Genre | : Mappings (Mathematics) |
ISBN | : |
Author | : Tosio Kato |
Publisher | : |
Total Pages | : 8 |
Release | : 1982 |
Genre | : |
ISBN | : |
Elementary proofs are given for the (known) theorems that (1) each point of superscript sigma(A) belongs to superscript sigma (e superscript A) if A is the generator of a C sub 0-semigroup E superscript tA) of linear operators on a Banach space x, and that (2) e superscript sigma(A) equal Sigma (e superscript A)/(0) if e superscript tA is a holomorphic semigroup. Also a large class of strongly continous groups e superscript tA on a Hilbert space H is given such that Sigma (A) is empty. Note that Sigma (e superscript A) is not empty, and is away from zero, if e superscript tA is a group. Some related remarks are given on the relationship between the spectral bound of A and the type of e superscript tA. (Author).
Author | : Carlos S. Kubrusly |
Publisher | : Springer Nature |
Total Pages | : 249 |
Release | : 2020-01-30 |
Genre | : Mathematics |
ISBN | : 3030331490 |
This textbook introduces spectral theory for bounded linear operators by focusing on (i) the spectral theory and functional calculus for normal operators acting on Hilbert spaces; (ii) the Riesz-Dunford functional calculus for Banach-space operators; and (iii) the Fredholm theory in both Banach and Hilbert spaces. Detailed proofs of all theorems are included and presented with precision and clarity, especially for the spectral theorems, allowing students to thoroughly familiarize themselves with all the important concepts. Covering both basic and more advanced material, the five chapters and two appendices of this volume provide a modern treatment on spectral theory. Topics range from spectral results on the Banach algebra of bounded linear operators acting on Banach spaces to functional calculus for Hilbert and Banach-space operators, including Fredholm and multiplicity theories. Supplementary propositions and further notes are included as well, ensuring a wide range of topics in spectral theory are covered. Spectral Theory of Bounded Linear Operators is ideal for graduate students in mathematics, and will also appeal to a wider audience of statisticians, engineers, and physicists. Though it is mostly self-contained, a familiarity with functional analysis, especially operator theory, will be helpful.