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Structure Of Hilbert Space Operators
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Book Synopsis Elements of Hilbert Spaces and Operator Theory by : Harkrishan Lal Vasudeva
Download or read book Elements of Hilbert Spaces and Operator Theory written by Harkrishan Lal Vasudeva and published by Springer. This book was released on 2017-03-27 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inner product spaces, linear operators, spectral theory and special classes of operators, and Banach spaces. On vector spaces, the structure of inner product is imposed. After discussing geometry of Hilbert spaces, its applications to diverse branches of mathematics have been studied. Along the way are introduced orthogonal polynomials and their use in Fourier series and approximations. Spectrum of an operator is the key to the understanding of the operator. Properties of the spectrum of different classes of operators, such as normal operators, self-adjoint operators, unitaries, isometries and compact operators have been discussed. A large number of examples of operators, along with their spectrum and its splitting into point spectrum, continuous spectrum, residual spectrum, approximate point spectrum and compression spectrum, have been worked out. Spectral theorems for self-adjoint operators, and normal operators, follow the spectral theorem for compact normal operators. The book also discusses invariant subspaces with special attention to the Volterra operator and unbounded operators. In order to make the text as accessible as possible, motivation for the topics is introduced and a greater amount of explanation than is usually found in standard texts on the subject is provided. The abstract theory in the book is supplemented with concrete examples. It is expected that these features will help the reader get a good grasp of the topics discussed. Hints and solutions to all the problems are collected at the end of the book. Additional features are introduced in the book when it becomes imperative. This spirit is kept alive throughout the book.
Book Synopsis Structure Of Hilbert Space Operators by : Chunlan Jiang
Download or read book Structure Of Hilbert Space Operators written by Chunlan Jiang and published by World Scientific. This book was released on 2006-03-01 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book exposes the internal structure of non-self-adjoint operators acting on complex separable infinite dimensional Hilbert space, by analyzing and studying the commutant of operators. A unique presentation of the theorem of Cowen-Douglas operators is given. The authors take the strongly irreducible operator as a basic model, and find complete similarity invariants of Cowen-Douglas operators by using K-theory, complex geometry and operator algebra tools.
Book Synopsis Harmonic Analysis of Operators on Hilbert Space by : Béla Sz Nagy
Download or read book Harmonic Analysis of Operators on Hilbert Space written by Béla Sz Nagy and published by Springer Science & Business Media. This book was released on 2010-09-01 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.
Book Synopsis Strongly Irreducible Operators on Hilbert Space by : Chun Lan Jiang
Download or read book Strongly Irreducible Operators on Hilbert Space written by Chun Lan Jiang and published by CRC Press. This book was released on 1998-05-01 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive treatment of strongly irreducible operators acting on a complex separable infinite dimensional Hilbert space, and to expose and reflect the internal structure of operators by analyzing and studying irreducibility of operators. Much of the material presented here appears in book form for the first time.
Book Synopsis Hilbert Space Operators by : Carlos S. Kubrusly
Download or read book Hilbert Space Operators written by Carlos S. Kubrusly and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained work on Hilbert space operators takes a problem-solving approach to the subject, combining theoretical results with a wide variety of exercises that range from the straightforward to the state-of-the-art. Complete solutions to all problems are provided. The text covers the basics of bounded linear operators on a Hilbert space and gradually progresses to more advanced topics in spectral theory and quasireducible operators. Written in a motivating and rigorous style, the work has few prerequisites beyond elementary functional analysis, and will appeal to graduate students and researchers in mathematics, physics, engineering, and related disciplines.
Book Synopsis A Primer on Hilbert Space Operators by : Piotr Sołtan
Download or read book A Primer on Hilbert Space Operators written by Piotr Sołtan and published by Springer. This book was released on 2018-09-04 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book concisely presents the fundamental aspects of the theory of operators on Hilbert spaces. The topics covered include functional calculus and spectral theorems, compact operators, trace class and Hilbert-Schmidt operators, self-adjoint extensions of symmetric operators, and one-parameter groups of operators. The exposition of the material on unbounded operators is based on a novel tool, called the z-transform, which provides a way to encode full information about unbounded operators in bounded ones, hence making many technical aspects of the theory less involved.
Author :Ruben A. Martinez-Avendano Publisher :Springer Science & Business Media ISBN 13 :0387485783 Total Pages :230 pages Book Rating :4.3/5 (874 download)
Book Synopsis An Introduction to Operators on the Hardy-Hilbert Space by : Ruben A. Martinez-Avendano
Download or read book An Introduction to Operators on the Hardy-Hilbert Space written by Ruben A. Martinez-Avendano and published by Springer Science & Business Media. This book was released on 2007-03-12 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an elementary and engaging introduction to operator theory on the Hardy-Hilbert space. It provides a firm foundation for the study of all spaces of analytic functions and of the operators on them. Blending techniques from "soft" and "hard" analysis, the book contains clear and beautiful proofs. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.
Book Synopsis Linear Systems and Operators in Hilbert Space by : Paul A. Fuhrmann
Download or read book Linear Systems and Operators in Hilbert Space written by Paul A. Fuhrmann and published by Courier Corporation. This book was released on 2014-01-15 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Three-part approach, with notes and references for each section, covers linear algebra and finite dimensional systems, operators in Hilbert space, and linear systems in Hilbert space. 1981 edition.
Book Synopsis Operators on Hilbert Space by : V. S. Sunder
Download or read book Operators on Hilbert Space written by V. S. Sunder and published by Springer. This book was released on 2016-08-05 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Hilbert Space by : N. Young
Download or read book An Introduction to Hilbert Space written by N. Young and published by Cambridge University Press. This book was released on 1988-07-21 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an introduction to the theory of Hilbert space and its applications. The notion of Hilbert space is central in functional analysis and is used in numerous branches of pure and applied mathematics. Dr Young has stressed applications of the theory, particularly to the solution of partial differential equations in mathematical physics and to the approximation of functions in complex analysis. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained. It is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). Thus it will make an excellent first course in Hilbert space theory at either undergraduate or graduate level and will also be of interest to electrical engineers and physicists, particularly those involved in control theory and filter design.
Book Synopsis Spectral Theory of Self-Adjoint Operators in Hilbert Space by : Michael Sh. Birman
Download or read book Spectral Theory of Self-Adjoint Operators in Hilbert Space written by Michael Sh. Birman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: It isn't that they can't see the solution. It is Approach your problems from the right end that they can't see the problem. and begin with the answers. Then one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be com pletely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order" , which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Book Synopsis Strongly Irreducible Operators on Hilbert Space by : ChunLan Jiang
Download or read book Strongly Irreducible Operators on Hilbert Space written by ChunLan Jiang and published by Taylor & Francis. This book was released on 2023-02-15 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive treatment of strongly irreducible operators acting on a complex separable infinite dimensional Hilbert space, and to expose and reflect the internal structure of operators by analyzing and studying irreducibility of operators. Much of the material presented here appears in book form for the first time.
Book Synopsis Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces by : L. Molnár
Download or read book Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces written by L. Molnár and published by Springer. This book was released on 2006-11-15 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: The territory of preserver problems has grown continuously within linear analysis. This book presents a cross-section of the modern theory of preservers on infinite dimensional spaces (operator spaces and function spaces) through the author's corresponding results. Special emphasis is placed on preserver problems concerning some structures of Hilbert space operators which appear in quantum mechanics. In addition, local automorphisms and local isometries of operator algebras and function algebras are discussed in detail.
Book Synopsis The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms by : Gilles Pisier
Download or read book The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms written by Gilles Pisier and published by American Mathematical Soc.. This book was released on 1996 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the recently developed duality theory of operator spaces (as developed by Effros-Ruan and Blecher-Paulsen) bounded operators are replaced by completely bounded ones, isomorphisms by complete isomorphisms, and Banach spaces by operator spaces. This allows for distinguishing between the various ways in which a given Banach space can be embedded isometrically into $B(H)$ (with $H$ being Hilbert). In this new category, several operator spaces which are isomorphic (as Banach spaces) to a Hilbert space play an important role. For instance the row and column Hilbert spaces and several other examples appearing naturally in the construction of the Boson or Fermion Fock spaces have been studied extensively. One of the main results of this memoir is the observation that there is a central object in this class: there is a unique self dual Hilbertian operator space (denoted by $OH$ ) which seems to play the same central role in the category of operator spaces that Hilbert spaces play in the category of Banach spaces. This new concept, called ``the operator Hilbert space'' and denoted by $OH$, is introduced and thoroughly studied in this volume.
Book Synopsis The Operator Hilbert Space OH, Complex Interpolation, and Tensor Norms by : Gilles Pisier
Download or read book The Operator Hilbert Space OH, Complex Interpolation, and Tensor Norms written by Gilles Pisier and published by American Mathematical Soc.. This book was released on 1996-07-02 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the recently developed duality theory of operator spaces (as developed by Effros-Ruan and Blecher-Paulsen) bounded operators are replaced by completely bounded ones, isomorphisms by complete isomorphisms, and Banach spaces by operator spaces. This allows for distinguishing between the various ways in which a given Banach space can be embedded isometrically into $B(H)$ (with $H$ being Hilbert). In this new category, several operator spaces which are isomorphic (as Banach spaces) to a Hilbert space play an important role. For instance the row and column Hilbert spaces and several other examples appearing naturally in the construction of the Boson or Fermion Fock spaces have been studied extensively. One of the main results of this memoir is the observation that there is a central object in this class: there is a unique self dual Hilbertian operator space (denoted by $OH$ ) which seems to play the same central role in the category of operator spaces that Hilbert spaces play in the category of Banach spaces. This new concept, called ``the operator Hilbert space'' and denoted by $OH$, is introduced and thoroughly studied in this volume.
Book Synopsis Hilbert Space Operators in Quantum Physics by : Jirí Blank
Download or read book Hilbert Space Operators in Quantum Physics written by Jirí Blank and published by Springer Science & Business Media. This book was released on 1999-04-23 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Market: Mathematicians, researchers, teachers, and graduate students specializing in quantum physics, mathematical physics, and applied mathematics. "I really enjoyed reading this work. It is very well written, by three real experts in the field. It stands quite alone....The translation is remarkably good." John R. Taylor, University of Colorado Based on lectures delivered over the past two decades, this book explains in detail the theory of linear Hilbert-space operators and its uses in quantum physics. The central mathematical tool of this book is the spectral theory of self-adjoint operators, which together with functional analysis and an introduction to the theory of operator sets and algebras, is used in a systematic analysis of the operator aspect of quantum theory. In addition, the theory of Hilbert-space operators is discussed in conjunction with various applications such as Schrodinger operators and scattering theory.
Book Synopsis Quantum Mechanics in Hilbert Space by : Eduard Prugovecki
Download or read book Quantum Mechanics in Hilbert Space written by Eduard Prugovecki and published by Courier Dover Publications. This book was released on 2006-12-01 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous, critical presentation of the mathematics of nonrelativistic quantum mechanics, this text is suitable for advanced undergraduate and graduate courses in functional analysis. Exercises, hints, solutions. 1981 edition.
