An Introduction To Local Spectral Theory
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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.
Fredholm And Local Spectral Theory Ii
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Author : Pietro Aiena
language : en
Publisher: Springer
Release Date : 2018-11-24
Fredholm And Local Spectral Theory Ii written by Pietro Aiena and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-24 with Mathematics categories.
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.
Fredholm And Local Spectral Theory With Applications To Multipliers
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Author : Pietro Aiena
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-08
Fredholm And Local Spectral Theory With Applications To Multipliers written by Pietro Aiena 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 2007-05-08 with Mathematics categories.
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.
Complex Analysis And Spectral Theory
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Author : H. Garth Dales
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-02-07
Complex Analysis And Spectral Theory written by H. Garth Dales 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 2020-02-07 with Education categories.
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.
Spectral Theory Of Linear Operators And Spectral Systems In Banach Algebras
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Author : Vladimir Müller
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11
Spectral Theory Of Linear Operators And Spectral Systems In Banach Algebras written by Vladimir Müller and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
Spectral theory is an important part of functional analysis.It has numerous appli cations in many parts of mathematics and physics including matrix theory, func tion theory, complex analysis, differential and integral equations, control theory and quantum physics. In recent years, spectral theory has witnessed an explosive development. There are many types of spectra, both for one or several commuting operators, with important applications, for example the approximate point spectrum, Taylor spectrum, local spectrum, essential spectrum, etc. The present monograph is an attempt to organize the available material most of which exists only in the form of research papers scattered throughout the literature. The aim is to present a survey of results concerning various types of spectra in a unified, axiomatic way. The central unifying notion is that of a regularity, which in a Banach algebra is a subset of elements that are considered to be "nice". A regularity R in a Banach algebra A defines the corresponding spectrum aR(a) = {A E C : a - ,\ rJ. R} in the same way as the ordinary spectrum is defined by means of invertible elements, a(a) = {A E C : a - ,\ rJ. Inv(A)}. Axioms of a regularity are chosen in such a way that there are many natural interesting classes satisfying them. At the same time they are strong enough for non-trivial consequences, for example the spectral mapping theorem.
Harmonic Morphisms Between Riemannian Manifolds
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Author : Paul Baird
language : en
Publisher: Oxford University Press
Release Date : 2003
Harmonic Morphisms Between Riemannian Manifolds written by Paul Baird 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 2003 with Mathematics categories.
This is an account in book form of the theory of harmonic morphisms between Riemannian manifolds.
Operator Algebras And Their Modules
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Author : David P. Blecher
language : en
Publisher: Oxford University Press
Release Date : 2004-10-07
Operator Algebras And Their Modules written by David P. Blecher 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 2004-10-07 with Mathematics categories.
This invaluable reference is the first to present the general theory of algebras of operators on a Hilbert space, and the modules over such algebras. The new theory of operator spaces is presented early on and the text assembles the basic concepts, theory and methodologies needed to equip a beginning researcher in this area. A major trend in modern mathematics, inspired largely by physics, is toward `noncommutative' or `quantized' phenomena. In functional analysis, this has appeared notably under the name of `operator spaces', which is a variant of Banach spaces which is particularly appropriate for solving problems concerning spaces or algebras of operators on Hilbert space arising in 'noncommutative mathematics'. The category of operator spaces includes operator algebras, selfadjoint (that is, C*-algebras) or otherwise. Also, most of the important modules over operator algebras are operator spaces. A common treatment of the subjects of C*-algebras, nonselfadjoint operator algebras, and modules over such algebras (such as Hilbert C*-modules), together under the umbrella of operator space theory, is the main topic of the book. A general theory of operator algebras, and their modules, naturally develops out of the operator space methodology. Indeed, operator space theory is a sensitive enough medium to reflect accurately many important noncommutative phenomena. Using recent advances in the field, the book shows how the underlying operator space structure captures, very precisely, the profound relations between the algebraic and the functional analytic structures involved. The rich interplay between spectral theory, operator theory, C*-algebra and von Neumann algebra techniques, and the influx of important ideas from related disciplines, such as pure algebra, Banach space theory, Banach algebras, and abstract function theory is highlighted. Each chapter ends with a lengthy section of notes containing a wealth of additional information.
The Structure Of Groups Of Prime Power Order
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Author : Charles Richard Leedham-Green
language : en
Publisher: Clarendon Press
Release Date : 2002
The Structure Of Groups Of Prime Power Order written by Charles Richard Leedham-Green and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
An important monograph summarizing the development of a classification system of finite p-groups.
The Mysteries Of The Real Prime
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Author : M. J. Shai Haran
language : en
Publisher: Oxford University Press
Release Date : 2001
The Mysteries Of The Real Prime written by M. J. Shai Haran 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 2001 with Language Arts & Disciplines categories.
Highly topical and original monograph, introducing the author's work on the Riemann zeta function and its adelic interpretation of interest to a wide range of mathematicians and physicists.
Characters Of Finite Coxeter Groups And Iwahori Hecke Algebras
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Author : Meinolf Geck
language : en
Publisher: Oxford University Press
Release Date : 2000
Characters Of Finite Coxeter Groups And Iwahori Hecke Algebras written by Meinolf Geck 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.
'An important book... The authors make full use of recent advances... The book is both a valuable resource for the expert and good starting point for the beginning researcher in this field... this is a very fine book which belongs on the shelves of anyone who is interested in the representation theory of Coxeter groups, Iwahori-Hecke algebras and, more generally, the groups of Lie type.' -Zentralblatt MATH'What makes the book especially valuable are the facts that the authors develop the various necessary theories nearly from the scratch... and that they include the algorithmic theory as well.' -Monatshefte för Mathematick'Written in an engaging and intelligible style... well structured and clearly printed.' -EMS'It will be a valuable reference for many years to come.' -Bulletin of the LMSFinite Coxeter groups and related structures arise naturally in several branches of mathematics, for example, Lie algebras or theory of knots and links. This is the first book which develops the character theory of finite Coxeter groups and Iwahori-Hecke algebras in a systematic way, ranging from classical results to recent developments.