An Introduction To Local Spectral Theory

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An Introduction to Local Spectral Theory

K. B. Laursen,Michael Neumann
An Introduction to Local Spectral Theory Book PDF

Author : K. B. Laursen,Michael Neumann
Publisher : Oxford University Press
Page : 610 pages
File Size : 48,7 Mb
Release : 2000
Category : Mathematics
ISBN : 0198523815

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An Introduction to Local Spectral Theory by K. B. Laursen,Michael Neumann Pdf

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.

Fredholm and Local Spectral Theory, with Applications to Multipliers

Pietro Aiena
Fredholm and Local Spectral Theory with Applications to Multipliers Book PDF

Author : Pietro Aiena
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 44,8 Mb
Release : 2007-05-08
Category : Mathematics
ISBN : 9781402025259

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Fredholm and Local Spectral Theory, with Applications to Multipliers by Pietro Aiena Pdf

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.

Fredholm and Local Spectral Theory II

Pietro Aiena
Fredholm and Local Spectral Theory II Book PDF

Author : Pietro Aiena
Publisher : Springer
Page : 546 pages
File Size : 40,6 Mb
Release : 2018-11-24
Category : Mathematics
ISBN : 9783030022662

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Fredholm and Local Spectral Theory II by Pietro Aiena Pdf

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 of Linear Operators

Vladimir Müller
Spectral Theory of Linear Operators Book PDF

Author : Vladimir Müller
Publisher : Springer Science & Business Media
Page : 439 pages
File Size : 42,7 Mb
Release : 2007-12-24
Category : Mathematics
ISBN : 9783764382650

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Spectral Theory of Linear Operators by Vladimir Müller Pdf

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.

Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation

Manuel Cepedello Boiso,Håkan Hedenmalm,Marinus A. Kaashoek,Alfonso Montes Rodríguez,Sergei Treil
Concrete Operators Spectral Theory Operators in Harmonic Analysis and Approximation Book PDF

Author : Manuel Cepedello Boiso,Håkan Hedenmalm,Marinus A. Kaashoek,Alfonso Montes Rodríguez,Sergei Treil
Publisher : Springer Science & Business Media
Page : 546 pages
File Size : 53,7 Mb
Release : 2013-11-04
Category : Mathematics
ISBN : 9783034806480

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Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation by Manuel Cepedello Boiso,Håkan Hedenmalm,Marinus A. Kaashoek,Alfonso Montes Rodríguez,Sergei Treil Pdf

This book contains a collection of research articles and surveys on recent developments on operator theory as well as its applications covered in the IWOTA 2011 conference held at Sevilla University in the summer of 2011. The topics include spectral theory, differential operators, integral operators, composition operators, Toeplitz operators, and more. The book also presents a large number of techniques in operator theory.

Spectral Theory and Its Applications

Bernard Helffer
Spectral Theory and Its Applications Book PDF

Author : Bernard Helffer
Publisher : Cambridge University Press
Page : 263 pages
File Size : 50,5 Mb
Release : 2013-01-17
Category : Mathematics
ISBN : 9781107032309

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Spectral Theory and Its Applications by Bernard Helffer Pdf

Introduces the basic tools in spectral analysis using numerous examples from the Schrödinger operator theory and various branches of physics.

Complex Analysis and Spectral Theory

H. Garth Dales,Dmitry Khavinson,Javad Mashreghi
Complex Analysis and Spectral Theory Book PDF

Author : H. Garth Dales,Dmitry Khavinson,Javad Mashreghi
Publisher : American Mathematical Soc.
Page : 280 pages
File Size : 41,8 Mb
Release : 2020-02-07
Category : Education
ISBN : 9781470446925

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Complex Analysis and Spectral Theory by H. Garth Dales,Dmitry Khavinson,Javad Mashreghi Pdf

This volume contains the proceedings of the Conference on Complex Analysis and Spectral Theory, in celebration of Thomas Ransford's 60th birthday, held from May 21–25, 2018, at Laval University, Québec, Canada. Spectral theory is the branch of mathematics devoted to the study of matrices and their eigenvalues, as well as their infinite-dimensional counterparts, linear operators and their spectra. Spectral theory is ubiquitous in science and engineering because so many physical phenomena, being essentially linear in nature, can be modelled using linear operators. On the other hand, complex analysis is the calculus of functions of a complex variable. They are widely used in mathematics, physics, and in engineering. Both topics are related to numerous other domains in mathematics as well as other branches of science and engineering. The list includes, but is not restricted to, analytical mechanics, physics, astronomy (celestial mechanics), geology (weather modeling), chemistry (reaction rates), biology, population modeling, economics (stock trends, interest rates and the market equilibrium price changes). There are many other connections, and in recent years there has been a tremendous amount of work on reproducing kernel Hilbert spaces of analytic functions, on the operators acting on them, as well as on applications in physics and engineering, which arise from pure topics like interpolation and sampling. Many of these connections are discussed in articles included in this book.

A Guide to Spectral Theory

Christophe Cheverry,Nicolas Raymond
A Guide to Spectral Theory Book PDF

Author : Christophe Cheverry,Nicolas Raymond
Publisher : Springer Nature
Page : 258 pages
File Size : 41,7 Mb
Release : 2021-05-06
Category : Mathematics
ISBN : 9783030674625

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A Guide to Spectral Theory by Christophe Cheverry,Nicolas Raymond Pdf

This textbook provides a graduate-level introduction to the spectral theory of linear operators on Banach and Hilbert spaces, guiding readers through key components of spectral theory and its applications in quantum physics. Based on their extensive teaching experience, the authors present topics in a progressive manner so that each chapter builds on the ones preceding. Researchers and students alike will also appreciate the exploration of more advanced applications and research perspectives presented near the end of the book. Beginning with a brief introduction to the relationship between spectral theory and quantum physics, the authors go on to explore unbounded operators, analyzing closed, adjoint, and self-adjoint operators. Next, the spectrum of a closed operator is defined and the fundamental properties of Fredholm operators are introduced. The authors then develop the Grushin method to execute the spectral analysis of compact operators. The chapters that follow are devoted to examining Hille-Yoshida and Stone theorems, the spectral analysis of self-adjoint operators, and trace-class and Hilbert-Schmidt operators. The final chapter opens the discussion to several selected applications. Throughout this textbook, detailed proofs are given, and the statements are illustrated by a number of well-chosen examples. At the end, an appendix about foundational functional analysis theorems is provided to help the uninitiated reader. A Guide to Spectral Theory: Applications and Exercises is intended for graduate students taking an introductory course in spectral theory or operator theory. A background in linear functional analysis and partial differential equations is assumed; basic knowledge of bounded linear operators is useful but not required. PhD students and researchers will also find this volume to be of interest, particularly the research directions provided in later chapters.

Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras

Vladimir Müller
Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras Book PDF

Author : Vladimir Müller
Publisher : Birkhäuser
Page : 390 pages
File Size : 55,5 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783034877886

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Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras by Vladimir Müller Pdf

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 and Analytic Geometry over Non-Archimedean Fields

Vladimir G. Berkovich
Spectral Theory and Analytic Geometry over Non Archimedean Fields Book PDF

Author : Vladimir G. Berkovich
Publisher : American Mathematical Soc.
Page : 169 pages
File Size : 54,5 Mb
Release : 2012-08-02
Category : Algebraic number theory
ISBN : 9780821890202

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Spectral Theory and Analytic Geometry over Non-Archimedean Fields by Vladimir G. Berkovich Pdf

The purpose of this book is to introduce a new notion of analytic space over a non-Archimedean field. Despite the total disconnectedness of the ground field, these analytic spaces have the usual topological properties of a complex analytic space, such as local compactness and local arcwise connectedness. This makes it possible to apply the usual notions of homotopy and singular homology. The book includes a homotopic characterization of the analytic spaces associated with certain classes of algebraic varieties and an interpretation of Bruhat-Tits buildings in terms of these analytic spaces. The author also studies the connection with the earlier notion of a rigid analytic space. Geometrical considerations are used to obtain some applications, and the analytic spaces are used to construct the foundations of a non-Archimedean spectral theory of bounded linear operators. This book requires a background at the level of basic graduate courses in algebra and topology, as well as some familiarity with algebraic geometry. It would be of interest to research mathematicians and graduate students working in algebraic geometry, number theory, and -adic analysis.

A Local Spectral Theory for Closed Operators

Ivan N. Erdelyi,Shengwang Wang
A Local Spectral Theory for Closed Operators Book PDF

Author : Ivan N. Erdelyi,Shengwang Wang
Publisher : Cambridge University Press
Page : 194 pages
File Size : 55,9 Mb
Release : 1985-08
Category : Mathematics
ISBN : 0521313147

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A Local Spectral Theory for Closed Operators by Ivan N. Erdelyi,Shengwang Wang Pdf

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.

Topological Algebras and their Applications

Alexander Katz
Topological Algebras and their Applications Book PDF

Author : Alexander Katz
Publisher : Walter de Gruyter GmbH & Co KG
Page : 317 pages
File Size : 48,5 Mb
Release : 2018-05-07
Category : Mathematics
ISBN : 9783110413557

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Topological Algebras and their Applications by Alexander Katz Pdf

Proceedings of the 8th International Conference of Topological Algebras and Their Applications (ICTAA-2014), held on May 26-30, 2014 in Playa de Villas de Mar Beach, dedicated to the memory of Anastasios Mallios (Athens, Greece). This series of conferences started in 1999 in Tartu, Estonia and were subsequently held in Rabat, Moroco (2000), Oulu, Finland (2001), Oaxaca, Mexico (2002), Bedlewo, Poland (2003), Athens, Greece (2005) and Tartu, Estonia (2008 and 2013). The topics of the conference include all areas of mathematics, connected with (preferably general) topological algebras and their applications, including all kinds of topological-algebraic structures as topological linear spaces, topological rings, topological modules, topological groups and semigroups; bornological-algebraic structures such as bornological linear spaces, bornological algebras, bornological groups, bornological rings and modules; algebraic and topological K-theory; topological module bundles, sheaves and others. Contents Some results on spectral properties of unital algebras and on the algebra of linear operators on a unital algebra Descriptions of all closed maximal one-sided ideals in topological algebras On non self-adjoint operators defined by Riesz bases in Hilbert and rigged Hilbert spaces Functional calculus on algebras of operators generated by a self-adjoint operator in Pontryagin space Π1 On Gelfand-Naimark type Theorems for unital abelian complex and real locally C*-, and locally JB-algebras Multipliers and strictly real topological algebras Multipliers in some perfect locally m-pseudo-convex algebras Wedderburn structure theorems for two-sided locally m-convex H*-algebras Homologically best modules in classical and quantized functional analysis Operator Grüss inequality Main embedding theorems for symmetric spaces of measurable functions Mapping class groups are linear Subnormable A-convex algebras Commutative BP*-algebras and Gelfand-Naimark’s theorem Discrete nonclosed subsets in maximally nondiscrete topological groups Faithfully representable topological *-algebras: some spectral properties On continuity of complementors in topological algebras Dominated ergodic theorem for isometries of non-commutative Lp-spaces, 1 p p ≠ 2 Ranks and the approximate n-th root property of C*-algebras Dense ideals in topological algebras: some results and open problems

Spectral Theory of Bounded Linear Operators

Carlos S. Kubrusly
Spectral Theory of Bounded Linear Operators Book PDF

Author : Carlos S. Kubrusly
Publisher : Springer Nature
Page : 249 pages
File Size : 44,6 Mb
Release : 2020-01-30
Category : Mathematics
ISBN : 9783030331498

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Spectral Theory of Bounded Linear Operators by Carlos S. Kubrusly Pdf

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.

Banach Algebras 97

Ernst Albrecht,Martin Mathieu
Banach Algebras 97 Book PDF

Author : Ernst Albrecht,Martin Mathieu
Publisher : Walter de Gruyter
Page : 576 pages
File Size : 53,9 Mb
Release : 2012-05-07
Category : Mathematics
ISBN : 9783110802009

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Banach Algebras 97 by Ernst Albrecht,Martin Mathieu Pdf

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.