A generalized spectral mapping theorem
Author | : Thiruvaiyaru V. Panchapagesan |
Publisher | : |
Total Pages | : 38 |
Release | : 1978 |
Genre | : |
ISBN | : |
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Author | : Thiruvaiyaru V. Panchapagesan |
Publisher | : |
Total Pages | : 38 |
Release | : 1978 |
Genre | : |
ISBN | : |
Author | : Ion Colojoara |
Publisher | : CRC Press |
Total Pages | : 254 |
Release | : 1968 |
Genre | : Mathematics |
ISBN | : 9780677014807 |
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 | : R. E. Harte |
Publisher | : |
Total Pages | : |
Release | : 1972 |
Genre | : |
ISBN | : |
Author | : Theodore W. Palmer |
Publisher | : Cambridge University Press |
Total Pages | : 820 |
Release | : 1994-03-25 |
Genre | : Mathematics |
ISBN | : 9780521366373 |
This is the first volume of a two volume set that provides a modern account of basic Banach algebra theory including all known results on general Banach *-algebras. This account emphasizes the role of *-algebraic structure and explores the algebraic results that underlie the theory of Banach algebras and *-algebras. The first volume, which contains previously unpublished results, is an independent, self-contained reference on Banach algebra theory. Each topic is treated in the maximum interesting generality within the framework of some class of complex algebras rather than topological algebras. Proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, particularly in noncommutative harmonic analysis, and an extensive bibliography. Volume II is forthcoming.
Author | : Henry R. Dowson |
Publisher | : |
Total Pages | : 444 |
Release | : 1978 |
Genre | : Banach spaces |
ISBN | : |
General spectral theory; Riesz operators; Hermitian operators; Prespectral operators; Well-bounded operators.
Author | : K. B. Laursen |
Publisher | : Oxford University Press |
Total Pages | : 610 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9780198523819 |
Modern local spectral theory is built on the classical spectral theorem, a fundamental result in single-operator theory and Hilbert spaces. This book provides an in-depth introduction to the natural expansion of this fascinating topic of Banach space operator theory. It gives complete coverage of the field, including the fundamental recent work by Albrecht and Eschmeier which provides the full duality theory for Banach space operators. One of its highlights are the many characterizations of decomposable operators, and of other related, important classes of operators, including identifications of distinguished parts, and results on permanence properties of spectra with respect to several types of similarity. Written in a careful and detailed style, it contains numerous examples, many simplified proofs of classical results, extensive references, and open problems, suitable for continued research.
Author | : Mihai Putinar |
Publisher | : |
Total Pages | : 8 |
Release | : 1980 |
Genre | : |
ISBN | : |
Author | : Gilbert Helmberg |
Publisher | : Elsevier |
Total Pages | : 362 |
Release | : 2014-11-28 |
Genre | : Science |
ISBN | : 1483164179 |
North-Holland Series in Applied Mathematics and Mechanics, Volume 6: Introduction to Spectral Theory in Hilbert Space focuses on the mechanics, principles, and approaches involved in spectral theory in Hilbert space. The publication first elaborates on the concept and specific geometry of Hilbert space and bounded linear operators. Discussions focus on projection and adjoint operators, bilinear forms, bounded linear mappings, isomorphisms, orthogonal subspaces, base, subspaces, finite dimensional Euclidean space, and normed linear spaces. The text then takes a look at the general theory of linear operators and spectral analysis of compact linear operators, including spectral decomposition of a compact selfadjoint operator, weakly convergent sequences, spectrum of a compact linear operator, and eigenvalues of a linear operator. The manuscript ponders on the spectral analysis of bounded linear operators and unbounded selfadjoint operators. Topics include spectral decomposition of an unbounded selfadjoint operator and bounded normal operator, functions of a unitary operator, step functions of a bounded selfadjoint operator, polynomials in a bounded operator, and order relation for bounded selfadjoint operators. The publication is a valuable source of data for mathematicians and researchers interested in spectral theory in Hilbert space.
Author | : Ioannis Antoniou |
Publisher | : CRC Press |
Total Pages | : 360 |
Release | : 2021-02-25 |
Genre | : Mathematics |
ISBN | : 1000657744 |
Nobel prize winner Ilya Prigogine writes in his preface: "Irreversibility is a challenge to mathematics...[which] leads to generalized functions and to an extension of spectral analysis beyond the conventional Hilbert space theory." Meeting this challenge required new mathematical formulations-obstacles met and largely overcome thanks primarily to the contributors to this volume." This compilation of works grew out of material presented at the "Hyperfunctions, Operator Theory and Dynamical Systems" symposium at the International Solvay Institutes for Physics and Chemistry in 1997. The result is a coherently organized collective work that moves from general, widely applicable mathematical methods to ever more specialized physical applications. Presented in two sections, part one describes Generalized Functions and Operator Theory, part two addresses Operator Theory and Dynamical Systems. The interplay between mathematics and physics is now more necessary than ever-and more difficult than ever, given the increasing complexity of theories and methods.