A Local Spectral Theory for Closed Operators
A Local Spectral Theory for Closed Operators

Author: Ivan N. Erdelyi

Publisher: Cambridge University Press

Published: 1985-08

Total Pages: 194

ISBN-13: 9780521313148

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This book, which is almost entirely devoted to unbounded operators, gives a unified treatment of the contemporary local spectral theory for unbounded closed operators on a complex Banach space. While the main part of the book is original, necessary background materials provided. There are some completely new topics treated, such as the complete spectral duality theory with the first comprehensive proof of the predual theorem, in two different versions. Also covered are spectral resolvents of various kinds (monotomic, strongly monotonic, almost localized, analytically invariant), and spectral decompositions with respect to the identity. The book concludes with an extensive reference list, including many papers published in the People's Republic of China, here brought to the attention of Western mathematicians for the first time. Pure mathematicians, especially those working in operator theory and functional analysis, will find this book of interest.

An Introduction to Local Spectral Theory
An Introduction to Local Spectral Theory

Author: K. B. Laursen

Publisher: Oxford University Press

Published: 2000

Total Pages: 610

ISBN-13: 9780198523819

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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.

A Local Spectral Theory for Closed Operators
A Local Spectral Theory for Closed Operators

Author: Ivan Erdelyi

Publisher:

Published: 2014-05-14

Total Pages: 190

ISBN-13: 9781107087699

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This book, which is almost entirely devoted to unbounded operators, gives a unified treatment of the contemporary local spectral theory for unbounded closed operators on a complex Banach space. While the main part of the book is original, necessary background materials provided. There are some completely new topics treated, such as the complete spectral duality theory with the first comprehensive proof of the predual theorem, in two different versions. Also covered are spectral resolvents of various kinds (monotomic, strongly monotonic, almost localized, analytically invariant), and spectral decompositions with respect to the identity. The book concludes with an extensive reference list, including many papers published in the People's Republic of China, here brought to the attention of Western mathematicians for the first time. Pure mathematicians, especially those working in operator theory and functional analysis, will find this book of interest.

Fredholm and Local Spectral Theory, with Applications to Multipliers
Fredholm and Local Spectral Theory, with Applications to Multipliers

Author: Pietro Aiena

Publisher: Springer Science & Business Media

Published: 2007-05-08

Total Pages: 452

ISBN-13: 1402025254

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A signi?cant sector of the development of spectral theory outside the classical area of Hilbert space may be found amongst at multipliers de?ned on a complex commutative Banach algebra A. Although the general theory of multipliers for abstract Banach algebras has been widely investigated by several authors, it is surprising how rarely various aspects of the spectral theory, for instance Fredholm theory and Riesz theory, of these important classes of operators have been studied. This scarce consideration is even more surprising when one observes that the various aspects of spectral t- ory mentioned above are quite similar to those of a normal operator de?ned on a complex Hilbert space. In the last ten years the knowledge of the spectral properties of multip- ers of Banach algebras has increased considerably, thanks to the researches undertaken by many people working in local spectral theory and Fredholm theory. This research activity recently culminated with the publication of the book of Laursen and Neumann [214], which collects almost every thing that is known about the spectral theory of multipliers.

A Local Spectral Theory for Closed Operators
A Local Spectral Theory for Closed Operators

Author: Ivan N. Erdelyi

Publisher:

Published: 1985

Total Pages: 192

ISBN-13: 9781107093935

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This book, which is almost entirely devoted to unbounded operators, gives a unified treatment of the contemporary local spectral theory for unbounded closed operators on a complex Banach space. While the main part of the book is original, necessary backgr.

Fredholm and Local Spectral Theory II
Fredholm and Local Spectral Theory II

Author: Pietro Aiena

Publisher: Springer

Published: 2018-11-24

Total Pages: 546

ISBN-13: 3030022668

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This monograph concerns the relationship between the local spectral theory and Fredholm theory of bounded linear operators acting on Banach spaces. The purpose of this book is to provide a first general treatment of the theory of operators for which Weyl-type or Browder-type theorems hold. The product of intensive research carried out over the last ten years, this book explores for the first time in a monograph form, results that were only previously available in journal papers. Written in a simple style, with sections and chapters following an easy, natural flow, it will be an invaluable resource for researchers in Operator Theory and Functional Analysis. The reader is assumed to be familiar with the basic notions of linear algebra, functional analysis and complex analysis.

Spectral Theory and Applications of Linear Operators and Block Operator Matrices
Spectral Theory and Applications of Linear Operators and Block Operator Matrices

Author: Aref Jeribi

Publisher: Springer

Published: 2015-07-04

Total Pages: 608

ISBN-13: 3319175661

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Examining recent mathematical developments in the study of Fredholm operators, spectral theory and block operator matrices, with a rigorous treatment of classical Riesz theory of polynomially-compact operators, this volume covers both abstract and applied developments in the study of spectral theory. These topics are intimately related to the stability of underlying physical systems and play a crucial role in many branches of mathematics as well as numerous interdisciplinary applications. By studying classical Riesz theory of polynomially compact operators in order to establish the existence results of the second kind operator equations, this volume will assist the reader working to describe the spectrum, multiplicities and localization of the eigenvalues of polynomially-compact operators.

Spectral Theory of Linear Operators
Spectral Theory of Linear Operators

Author: Vladimir Müller

Publisher: Springer Science & Business Media

Published: 2007-12-24

Total Pages: 444

ISBN-13: 3764382651

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This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. Many results appear here for the first time in a monograph.

Spectral Theory of Bounded Linear Operators
Spectral Theory of Bounded Linear Operators

Author: Carlos S. Kubrusly

Publisher: Springer Nature

Published: 2020-01-30

Total Pages: 249

ISBN-13: 3030331490

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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.