Spectral Decompositions on Banach Spaces PDF Download

Author: I. Erdelyi
Publisher: Springer
ISBN: 3540369910
Category : Mathematics
Languages : en
Pages : 130

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Author: Jörg Eschmeier
Publisher: Oxford University Press
ISBN: 9780198536673
Category : Language Arts & Disciplines
Languages : en
Pages : 378

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Book Description
Rapid developments in multivariable spectral theory have led to important and fascinating results which also have applications in other mathematical disciplines. In this book, various concepts from function theory and complex analytic geometry are drawn together to give a new approach to concrete spectral computations and give insights into new developments in the spectral theory of linear operators. Classical results from cohomology theory of Banach algebras, multidimensional spectral theory, and complex analytic geometry have been freshly interpreted using the language of homological algebra. The advantages of this approach are illustrated by a variety of examples, unexpected applications, and conceptually new ideas that should stimulate further research among mathematicians.

Author: I. Erdelyi
Publisher:
ISBN: 9783662201930
Category :
Languages : en
Pages : 134

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Author: Ridgley Lange
Publisher: American Mathematical Soc.
ISBN: 082185139X
Category : Mathematics
Languages : en
Pages : 288

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Book Description
Aimed at a general mathematical audience, this book provides a careful exposition of developments in the theory of spectral decomposition. Bringing the reader from the basics up to the level of current research in the area at the time of writing, Lange and Wang present an accessible account of the techniques used in the theory and applications of decomposable operators and related classes of operators. The book begins with a discussion of criteria for decomposable and related types of operators, and an analysis that relates and distinguishes among them. Perturbation theory of decomposable and other operators, applications to classical Hilberty space operators, quasisimilarity, and a new class of weakly decomposable operators are also discussed. The book closes with an exposition of some classical theories on invariant subspaces for subdecomposable and hyponormal operators, and a presentation of the parallel spectral theory of commuting systems.

Author: Florian-Horia Vasilescu
Publisher: Springer Science & Business Media
ISBN: 9789027713766
Category : Mathematics
Languages : en
Pages : 398

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Author: Ivan Erdelyi
Publisher: Springer
ISBN: 9780387085258
Category : Banach spaces
Languages : en
Pages : 122

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Author: V.S. Sunder
Publisher: Springer Science & Business Media
ISBN: 9783764358921
Category : Mathematics
Languages : en
Pages : 260

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Book Description
In an elegant and concise fashion, this book presents the concepts of functional analysis required by students of mathematics and physics. It begins with the basics of normed linear spaces and quickly proceeds to concentrate on Hilbert spaces, specifically the spectral theorem for bounded as well as unbounded operators in separable Hilbert spaces. While the first two chapters are devoted to basic propositions concerning normed vector spaces and Hilbert spaces, the third chapter treats advanced topics which are perhaps not standard in a first course on functional analysis. It begins with the Gelfand theory of commutative Banach algebras, and proceeds to the Gelfand-Naimark theorem on commutative C*-algebras. A discussion of representations of C*-algebras follows, and the final section of this chapter is devoted to the Hahn-Hellinger classification of separable representations of commutative C*-algebras. After this detour into operator algebras, the fourth chapter reverts to more standard operator theory in Hilbert space, dwelling on topics such as the spectral theorem for normal operators, the polar decomposition theorem, and the Fredholm theory for compact operators. A brief introduction to the theory of unbounded operators on Hilbert space is given in the fifth and final chapter. There is a voluminous appendix whose purpose is to fill in possible gaps in the reader's background in various areas such as linear algebra, topology, set theory and measure theory. The book is interspersed with many exercises, and hints are provided for the solutions to the more challenging of these.

Author: Earl R. Berkson
Publisher: Cambridge University Press
ISBN: 9780521364379
Category : Mathematics
Languages : en
Pages : 370

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Book Description
Throughout the acedemic year 1986-7, the University of Illinois hosted a symposium on mathematical analysis attended by some of the leading figures in the field. This resulting book lays emphasis on the synthesis of modern and classical analysis. The contributed articles cover the mainstream topics and will be essential to researchers in mathematical analysis.

Author: Michiel Hazewinkel
Publisher: Springer Science & Business Media
ISBN: 0306483734
Category : Mathematics
Languages : en
Pages : 564

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Book Description
This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

Author: Dumitru Gaspar
Publisher: Springer Science & Business Media
ISBN: 3764373148
Category : Mathematics
Languages : en
Pages : 351

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Book Description
This book offers peer-reviewed articles from the 19th International Conference on Operator Theory, Summer 2002. It contains recent developments in a broad range of topics from operator theory, operator algebras and their applications, particularly to differential analysis, complex functions, ergodic theory, mathematical physics, matrix analysis, and systems theory. The book covers a large variety of topics including single operator theory, C*-algebras, diffrential operators, integral transforms, stochastic processes and operators, and more.