Spectral Mapping Theorems For Subnormal Operators
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Spectral Mapping Theorems For Subnormal Operators
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Author : James Joseph Dudziak
language : en
Publisher:
Release Date : 1983
Spectral Mapping Theorems For Subnormal Operators written by James Joseph Dudziak and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mappings (Mathematics) categories.
The Theory Of Subnormal Operators
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Author : John B. Conway
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
The Theory Of Subnormal Operators written by John B. Conway and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
"In a certain sense, subnormal operators were introduced too soon because the theory of function algebras and rational approximation was also in its infancy and could not be properly used to examine the class of operators. The progress in the last several years grew out of applying the results of rational approximation." from the Preface. This book is the successor to the author's 1981 book on the same subject. In addition to reflecting the great strides in the development of subnormal operator theory since the first book, the present work is oriented towards rational functions rather than polynomials. Although the book is a research monograph, it has many of the traits of a textbook including exercises. The book requires background in function theory and functional analysis, but is otherwise fairly self-contained. The first few chapters cover the basics about subnormal operator theory and present a study of analytic functions on the unit disk. Other topics included are: some results on hypernormal operators, an exposition of rational approximation interspersed with applications to operator theory, a study of weak-star rational approximation, a set of results that can be termed structure theorems for subnormal operators, and a proof that analytic bounded point evaluations exist.
Subnormal Operators And Representations Of Algebras Of Bounded Analytic Functions And Other Uniform Algebras
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Author : Thomas L. Miller
language : en
Publisher: American Mathematical Soc.
Release Date : 1986
Subnormal Operators And Representations Of Algebras Of Bounded Analytic Functions And Other Uniform Algebras written by Thomas L. Miller and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
The present memoir lies between operator theory and function theory of one complex variable. Motivated by refinements of the analytic functional calculus of a subnormal operator, the authors are rapidly directed towards difficult problems of hard analysis. Quite specifically, the basic objects to be investigated in this paper are the unital (continuous) algebra homomorphisms [lowercase Greek]Pi : [italic]H[exponent infinity symbol]([italic]G) [rightwards arrow] [italic]L([italic]H), with the additional property that [lowercase Greek]Pi([italic]z) is a subnormal operator.
A Functional Calculus For Subnormal Operators Ii
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Author : John B. Conway
language : en
Publisher: American Mathematical Soc.
Release Date : 1977
A Functional Calculus For Subnormal Operators Ii written by John B. Conway and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Mathematics categories.
Let S be a subnormal operator on a Hilbert space [script]H with minimal normal extension [italic]N operating on [italic]K, and let [lowercase Greek]Mu be a scalar valued spectral measure for [italic]N. If [italic]P[infinity symbol]([lowercase Greek]Mu) denotes the weak star closure of the polynomials in [italic]L[infinity symbol]([lowercase Greek]Mu) = [italic]L1[infinity symbol]([lowercase Greek]Mu) then for [script]f in [italic]P[infinity symbol]([lowercase Greek]Mu) it follows that [script]f([italic]N) leaves [script]H invariant; if [script]f([italic]S) is defined as the restriction of [script]f([italic]N) to [script]H then a functional calculus for [italic]S is obtained. This functional calculus is investigated in this paper.
An Introduction To Local Spectral Theory
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Author : K. B. Laursen
language : en
Publisher: Oxford University Press
Release Date : 2000
An Introduction To Local Spectral Theory written by K. B. Laursen and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
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, whose pioneers include Dunford, Bishop, Foias, and others. Assuming only modest prerequisites of its readership, 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. It is highlighted by many characterizations of decomposable operators, and of other related, important classes of operators, as well as an in-depth study of their spectral properties, including identifications of distinguished parts, and results on permanence properties of spectra with respect to several types of similarity. Also found is a thorough and quite elementary treatment of the modern single- operator duality theory; this theory has many applications, both to general issues of classification and to such celebrated problems as the invariant subspace problems. A long chapter - almost a book in itself - is devoted to the use of local spectral theory in the study of spectral properties of multipliers and convolution operators. Another one describes its connections to automatic continuity theory. Written in a careful and detailed style, it contains numerous examples, many simplified proofs of classical results, and extensive references. It concludes with a list of interesting open problems, suitable for continued research.
Operators And Function Theory
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Author : S.C. Power
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Operators And Function Theory written by S.C. Power and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In the modern study of Hilbert space operators there has been an increasingly subtle involvement with analytic function theory. This is evident in the analysis of subnormal operators, Toeplitz operators and Hankel operators, for example. On the other hand the operator theoretic viewpoint of interpolation by analytic functions is a powerful one. There has been significant activity in recent years, within these enriching interactions, and the time seemed right for an overview ot the main lines of development. The Advanced Study Institute 'Operators and Function Theory' in Lancaster, 1984, was devoted to this, and this book contains ex panded versions (and one contraction) of the main lecture prog ramme. These varied articles, by prominent researchers, include, for example, a survey of recent results on subnormal operators, recent work of Soviet mathematicians on Hankel and Toeplitz operators, expositions of the decomposition theory and inter polation theory for Bergman, Besov and Bloch spaces, with applic ations for special operators, the Krein space approach to inter polation problems, •• and much more. It is hoped that these proceedings will bring all this lively mathematics to a wider audience. Sincere thanks are due to the Scientific Committee of the North Atlantic Treaty Organisation for the generous support that made the institute possible, and to the London Mathematical Society and the British Council for important additional support. Warm thanks also go to Barry Johnson and the L.M.S. for early guidance, and to my colleague Graham Jameson for much organisational support.
A Spectral Theory Of Noncommuting Operators
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Author : Rongwei Yang
language : en
Publisher: Springer Nature
Release Date : 2024-03-25
A Spectral Theory Of Noncommuting Operators written by Rongwei Yang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-25 with Mathematics categories.
The main goal of this book is to describe various aspects of the theory of joint spectra for matrices and linear operators. It is suitable for a graduate-level topic course in spectral theory and/or representation theory. The first three chapters can also be adopted for an advanced course in linear algebra. Centered around the concept of projective spectrum, the book presents a coherent treatment of fundamental elements from a wide range of mathematical disciplines, such as complex analysis, complex dynamics, differential geometry, functional analysis, group theory, and Lie algebras. Researchers and students, particularly those who aspire to gain a bigger picture of mathematics, will find this book both informative and resourceful.
Operator Theory By Example
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Author : Stephan Ramon Garcia
language : en
Publisher: Oxford University Press
Release Date : 2023-02-09
Operator Theory By Example written by Stephan Ramon Garcia and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-09 with Science categories.
Aimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory. Rather than discuss the subject in the abstract, this textbook covers the subject through twenty examples of a wide variety of operators, discussing the norm, spectrum, commutant, invariant subspaces, and interesting properties of each operator. The text is supplemented by over 600 end-of-chapter exercises, designed to help the reader master the topics covered in the chapter, as well as providing an opportunity to further explore the vast operator theory literature. Each chapter also contains well-researched historical facts which place each chapter within the broader context of the development of the field as a whole.
Lectures On Hyponormal Operators
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Author : Mihai Putinar
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Lectures On Hyponormal Operators written by Mihai Putinar and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The present lectures are based on a course deli vered by the authors at the Uni versi ty of Bucharest, in the winter semester 1985-1986. Without aiming at completeness, the topics selected cover all the major questions concerning hyponormal operators. Our main purpose is to provide the reader with a straightforward access to an active field of research which is strongly related to the spectral and perturbation theories of Hilbert space operators, singular integral equations and scattering theory. We have in view an audience composed especially of experts in operator theory or integral equations, mathematical physicists and graduate students. The book is intended as a reference for the basic results on hyponormal operators, but has the structure of a textbook. Parts of it can also be used as a second year graduate course. As prerequisites the reader is supposed to be acquainted with the basic principles of functional analysis and operator theory as covered for instance by Reed and Simon [1]. A t several stages of preparation of the manuscript we were pleased to benefit from proper comments made by our cOlleagues: Grigore Arsene, Tiberiu Constantinescu, Raul Curto, Jan Janas, Bebe Prunaru, Florin Radulescu, Khrysztof Rudol, Konrad Schmudgen, Florian-Horia Vasilescu. We warmly thank them all. We are indebted to Professor Israel Gohberg, the editor of this series, for his constant encouragement and his valuable mathematical advice. We wish to thank Mr. Benno Zimmermann, the Mathematics Editor at Birkhauser Verlag, for cooperation and assistance during the preparation of the manuscript.
Invertibility And Singularity For Bounded Linear Operators
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Author : Robin Harte
language : en
Publisher: Courier Dover Publications
Release Date : 2016-11-16
Invertibility And Singularity For Bounded Linear Operators written by Robin Harte and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-16 with Mathematics categories.
Suitable for courses in functional analysis and a valuble resource for researchers, this introductory treatment is based on the open mapping theorem, Hahn-Banach theorem, dual space construction, enlargement of normed space, and Liouville's theorem. 1988 edition.