Invitation To Linear Operators From Matrices To Bounded Linear Operators On A Hilbert Space

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Invitation to Linear Operators From Matrices to Bounded Linear Operators on a Hilbert Space

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Author by : Takayuki Furuta
Languange Used : English, France, Spanish, Italia and chinese
Page : 272
Isbn : 9780415267991
Identifier : 0415267994
Release : 2001-07-26
Publisher by : CRC Press
Category : Mathematics
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Description : Read Now Invitation To Linear Operators by Takayuki Furuta and you can download with pub, pdf, txt, doc, and more file format with free account. most books on linear operators are not easy to follow for students and researchers without an extensive background in mathematics. self-contained and using only matrix theory, invitation to linear operators: from matricies to bounded linear operators on a hilbert space explains in easy-to-follow steps a variety of interesting recent results on linear operators on a hilbert space. the author first states the important properties of a hilbert space, then sets out the fundamental properties of bounded linear operators on a hilbert space. the final section presents some of the more recent developments in bounded linear operators.

Operator Inequalities

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Author by : Schroder
Languange Used : English, France, Spanish, Italia and chinese
Page : 366
Isbn : 0080956556
Identifier : 9780080956558
Release : 1980-09-01
Publisher by : Academic Press
Category : Computers
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Contributions to Operator Theory and Its Applications The Tsuyoshi Ando Anniversary Volume

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Author by : Takayuki Furuta
Languange Used : English, France, Spanish, Italia and chinese
Page : 231
Isbn :
Identifier : UOM:39015028912726
Release : 1993
Publisher by : Birkhauser
Category : Mathematics
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Functional Analysis Spectral Theory

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Author by : V.S. Sunder
Languange Used : English, France, Spanish, Italia and chinese
Page : 241
Isbn : 9783764358921
Identifier : 3764358920
Release : 1997
Publisher by : Springer Science & Business Media
Category : Mathematics
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Description : Read Now Functional Analysis by V.S. Sunder and you can download with pub, pdf, txt, doc, and more file format with free account. 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.

Linear Operators in Hilbert Space

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Author by : Jean Louis Soulé
Languange Used : English, France, Spanish, Italia and chinese
Page : 40
Isbn : 9780677301754
Identifier : 0677301758
Release : 1968
Publisher by : CRC Press
Category : Mathematics
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Spectral Theory of Block Operator Matrices and Applications

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Author by : Christiane Tretter
Languange Used : English, France, Spanish, Italia and chinese
Page : 296
Isbn : 1908979321
Identifier : 9781908979322
Release : 2008-10-15
Publisher by : World Scientific
Category : Science
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Description : Read Now Spectral Theory Of Block Operator Matrices And Applications by Christiane Tretter and you can download with pub, pdf, txt, doc, and more file format with free account. this book presents a wide panorama of methods to investigate the spectral properties of block operator matrices. particular emphasis is placed on classes of block operator matrices to which standard operator theoretical methods do not readily apply: non-self-adjoint block operator matrices, block operator matrices with unbounded entries, non-semibounded block operator matrices, and classes of block operator matrices arising in mathematical physics. the main topics include: localization of the spectrum by means of new concepts of numerical range; investigation of the essential spectrum; variational principles and eigenvalue estimates; block diagonalization and invariant subspaces; solutions of algebraic riccati equations; applications to spectral problems from magnetohydrodynamics, fluid mechanics, and quantum mechanics. contents:bounded block operator matrices:the quadratic numerical rangespecial classes of block operator matricesspectral inclusionestimates of the resolventcorners of the quadratic numerical rangeschur complements and their factorizationblock diagonalizationspectral supporting subspacesvariational principles for eigenvalues in gapsj-self-adjoint block operator matricesthe block numerical rangenumerical ranges of operator polynomialsgershgorin's theorem for block operator matricesunbounded block operator matrices:relative boundedness and relative compactnessclosedness and closability of block operator matricesspectrum and resolventthe essential spectrumspectral inclusionsymmetric and j-symmetric block operator matricesdichotomous block operator matrices and riccati equationsblock diagonalization and half range completenessuniqueness results for solutions of riccati equationsvariational principleseigenvalue estimatesapplications in mathematical physics:upper dominant block operator matrices in magnetohydrodynamicsdiagonally dominant block operator matrices in fluid mechanicsoff-diagonally dominant block operator matrices in quantum mechanics readership: mathematicians, physicists and engineers. keywords:operator theory;spectral theory;eigenvalues;differential equations;riccati equations;numerical range;mathematical physics;matrix theorykey features:challenging spectral problems to which standard methods do not applynew results even in the finite dimensional casemany illustrating exampleswide range of possible applicationsreviews:“this book is a valuable addition to the literature and will be of great help for those working in this field already as well as for people looking for an interesting introduction to the topic.”mathematical reviews

Unbounded Functionals in the Calculus of Variations Representation, Relaxation, and Homogenization

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Author by : Luciano Carbone
Languange Used : English, France, Spanish, Italia and chinese
Page : 408
Isbn : 9781420035582
Identifier : 1420035584
Release : 2001-12-12
Publisher by : CRC Press
Category : Mathematics
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Description : Read Now Unbounded Functionals In The Calculus Of Variations by Luciano Carbone and you can download with pub, pdf, txt, doc, and more file format with free account. over the last few decades, research in elastic-plastic torsion theory, electrostatic screening, and rubber-like nonlinear elastomers has pointed the way to some interesting new classes of minimum problems for energy functionals of the calculus of variations. this advanced-level monograph addresses these issues by developing the framework of a general theory of integral representation, relaxation, and homogenization for unbounded functionals. the first part of the book builds the foundation for the general theory with concepts and tools from convex analysis, measure theory, and the theory of variational convergences. the authors then introduce some function spaces and explore some lower semicontinuity and minimization problems for energy functionals. next, they survey some specific aspects the theory of standard functionals. the second half of the book carefully develops a theory of unbounded, translation invariant functionals that leads to results deeper than those already known, including unique extension properties, representation as integrals of the calculus of variations, relaxation theory, and homogenization processes. in this study, some new phenomena are pointed out. the authors' approach is unified and elegant, the text well written, and the results intriguing and useful, not just in various fields of mathematics, but also in a range of applied mathematics, physics, and material science disciplines.

Spectral Theory and Nonlinear Functional Analysis

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Author by : Julian Lopez-Gomez
Languange Used : English, France, Spanish, Italia and chinese
Page : 280
Isbn : 1420035509
Identifier : 9781420035506
Release : 2001-03-28
Publisher by : CRC Press
Category : Mathematics
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Description : Read Now Spectral Theory And Nonlinear Functional Analysis by Julian Lopez-Gomez and you can download with pub, pdf, txt, doc, and more file format with free account. this research note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure of the set of zeroes of a general class of nonlinear operators. it features the construction of an optimal algebraic/analytic invariant for calculating the leray-schauder degree, new methods for solving nonlinear equations in banach spaces, and general properties of components of solutions sets presented with minimal use of topological tools. the author also gives several applications of the abstract theory to reaction diffusion equations and systems. the results presented cover a thirty-year period and include recent, unpublished findings of the author and his coworkers. appealing to a broad audience, spectral theory and nonlinear functional analysis contains many important contributions to linear algebra, linear and nonlinear functional analysis, and topology and opens the door for further advances.

Introductory Functional Analysis with Applications

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Author by : Kreyszig
Languange Used : English, France, Spanish, Italia and chinese
Page : 704
Isbn : 9788126511914
Identifier : 8126511915
Release : 2007-03-01
Publisher by : John Wiley & Sons
Category : Functional analysis
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A First Course in Functional Analysis Theory and Applications

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Author by : Rabindranath Sen
Languange Used : English, France, Spanish, Italia and chinese
Page : 486
Isbn : 1783083247
Identifier : 9781783083244
Release : 2014-11-01
Publisher by : Anthem Press
Category : Mathematics
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Description : Read Now A First Course In Functional Analysis by Rabindranath Sen and you can download with pub, pdf, txt, doc, and more file format with free account. this book provides the reader with a comprehensive introduction to functional analysis. topics include normed linear and hilbert spaces, the hahn-banach theorem, the closed graph theorem, the open mapping theorem, linear operator theory, the spectral theory, and a brief introduction to the lebesgue measure. the book explains the motivation for the development of these theories, and applications that illustrate the theories in action. applications in optimal control theory, variational problems, wavelet analysis and dynamical systems are also highlighted. ‘a first course in functional analysis’ will serve as a ready reference to students not only of mathematics, but also of allied subjects in applied mathematics, physics, statistics and engineering.

Operators on Hilbert Space

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Author by : V. S. Sunder
Languange Used : English, France, Spanish, Italia and chinese
Page : 100
Isbn : 9811018162
Identifier : 9789811018169
Release : 2016-08-05
Publisher by : Springer
Category : Mathematics
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Description : Read Now Operators On Hilbert Space by V. S. Sunder and you can download with pub, pdf, txt, doc, and more file format with free account. the primarily objective of the book is to serve as a primer on the theory of bounded linear operators on separable hilbert space. the book presents the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus. it discusses a proof without digressing into a course on the gelfand theory of commutative banach algebras. the book also introduces the reader to the basic facts concerning the various von neumann–schatten ideals, the compact operators, the trace-class operators and all bounded operators.

Invitation to C*-algebras and Topological Dynamics

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Author by : Jun Tomiyama
Languange Used : English, France, Spanish, Italia and chinese
Page : 167
Isbn : 9789971503383
Identifier : 9971503387
Release : 1987
Publisher by : World Scientific
Category : Science
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Description : Read Now Invitation To C* Algebras And Topological Dynamics by Jun Tomiyama and you can download with pub, pdf, txt, doc, and more file format with free account. this book is an exposition on the interesting interplay between topological dynamics and the theory of c*-algebras. researchers working in topological dynamics from various fields in mathematics are becoming more and more interested in this kind of algebraic approach of dynamics. this book is designed to present to the readers the subject in an elementary way, including also results of recent developments.