Commutation Properties Of Hilbert Space Operators And Related Topics

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Commutation Properties Of Hilbert Space Operators And Related Topics

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Author : Calvin R. Putnam
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Commutation Properties Of Hilbert Space Operators And Related Topics written by Calvin R. Putnam 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 2012-12-06 with Mathematics categories.

What could be regarded as the beginning of a theory of commutators AB - BA of operators A and B on a Hilbert space, considered as a dis cipline in itself, goes back at least to the two papers of Weyl [3] {1928} and von Neumann [2] {1931} on quantum mechanics and the commuta tion relations occurring there. Here A and B were unbounded self-adjoint operators satisfying the relation AB - BA = iI, in some appropriate sense, and the problem was that of establishing the essential uniqueness of the pair A and B. The study of commutators of bounded operators on a Hilbert space has a more recent origin, which can probably be pinpointed as the paper of Wintner [6] {1947}. An investigation of a few related topics in the subject is the main concern of this brief monograph. The ensuing work considers commuting or "almost" commuting quantities A and B, usually bounded or unbounded operators on a Hilbert space, but occasionally regarded as elements of some normed space. An attempt is made to stress the role of the commutator AB - BA, and to investigate its properties, as well as those of its components A and B when the latter are subject to various restrictions. Some applica tions of the results obtained are made to quantum mechanics, perturba tion theory, Laurent and Toeplitz operators, singular integral trans formations, and Jacobi matrices.

Commutation Properties Of Hilbert Space Operators And Related Topics

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Author : C. R. Putnam
language : it
Publisher:
Release Date : 1967

Commutation Properties Of Hilbert Space Operators And Related Topics written by C. R. Putnam and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.

Hilbert Space Operators

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Author : Carlos S. Kubrusly
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Hilbert Space Operators written by Carlos S. Kubrusly 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 2012-12-06 with Mathematics categories.

This is a problem book on Hilbert space operators (Le. , on bounded linear transformations of a Hilbert space into itself) where theory and problems are investigated together. We tre!l:t only a part of the so-called single operator theory. Selected prob lems, ranging from standard textbook material to points on the boundary of the subject, are organized into twelve chapters. The book begins with elementary aspects of Invariant Subspaces for operators on Banach spaces 1. Basic properties of Hilbert Space Operators are introduced in in Chapter Chapter 2, Convergence and Stability are considered in Chapter 3, and Re ducing Subspaces is the theme of Chapter 4. Primary results about Shifts on Hilbert space comprise Chapter 5. These are introductory chapters where the majority of the problems consist of auxiliary results that prepare the ground for the next chapters. Chapter 6 deals with Decompositions for Hilbert space contractions, Chapter 7 focuses on Hyponormal Operators, and Chapter 8 is concerned with Spectral Properties of operators on Banach and Hilbert spaces. The next three chapters (as well as Chapter 6) carry their subjects from an introductory level to a more advanced one, including some recent results. Chapter 9 is about Paranormal Operators, Chapter 10 covers Proper Contractions, and Chapter 11 searches through Quasi reducible Operators. The final Chapter 12 commemorates three decades of The Lomonosov Theorem on nontrivial hyperinvariant subspaces for compact operators.

Commutation Properties Of Hilbert Space Operators And Related Topics

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Author : C. R. Putnam
language : de
Publisher:
Release Date : 1967

Commutation Properties Of Hilbert Space Operators And Related Topics written by C. R. Putnam and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.

Commutation Properties Of Hilbert Space Operators

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Author :
language : en
Publisher:
Release Date : 1965

Commutation Properties Of Hilbert Space Operators written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with categories.

Elements Of Operator Theory

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Author : Carlos S. Kubrusly
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Elements Of Operator Theory written by Carlos S. Kubrusly 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 2013-03-14 with Mathematics categories.

{\it Elements of Operatory Theory} is aimed at graduate students as well as a new generation of mathematicians and scientists who need to apply operator theory to their field. Written in a user-friendly, motivating style, fundamental topics are presented in a systematic fashion, i.e., set theory, algebraic structures, topological structures, Banach spaces, Hilbert spaces, culminating with the Spectral Theorem, one of the landmarks in the theory of operators on Hilbert spaces. The exposition is concept-driven and as much as possible avoids the formula-computational approach. Key features of this largely self-contained work include: * required background material to each chapter * fully rigorous proofs, over 300 of them, are specially tailored to the presentation and some are new * more than 100 examples and, in several cases, interesting counterexamples that demonstrate the frontiers of an important theorem * over 300 problems, many with hints * both problems and examples underscore further auxiliary results and extensions of the main theory; in this non-traditional framework, the reader is challenged and has a chance to prove the principal theorems anew This work is an excellent text for the classroom as well as a self-study resource for researchers. Prerequisites include an introduction to analysis and to functions of a complex variable, which most first-year graduate students in mathematics, engineering, or another formal science have already acquired. Measure theory and integration theory are required only for the last section of the final chapter.

Quantum Mechanics In Hilbert Space

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Author :
language : en
Publisher: Academic Press
Release Date : 2003-02-13

Quantum Mechanics In Hilbert Space written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-02-13 with Mathematics categories.

Quantum Mechanics in Hilbert Space

Operators And Representation Theory

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Author : Palle E.T. Jorgensen
language : en
Publisher: Courier Dover Publications
Release Date : 2017-05-22

Operators And Representation Theory written by Palle E.T. Jorgensen and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-22 with Science categories.

Three-part treatment covers background material on definitions, terminology, operators in Hilbert space domains of representations, operators in the enveloping algebra, spectral theory; and covariant representation and connections. 2017 edition.

Integration In Hilbert Space

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Author : A. V. Skorohod
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Integration In Hilbert Space written by A. V. Skorohod 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 2012-12-06 with Mathematics categories.

Integration in function spaces arose in probability theory when a gen eral theory of random processes was constructed. Here credit is cer tainly due to N. Wiener, who constructed a measure in function space, integrals-with respect to which express the mean value of functionals of Brownian motion trajectories. Brownian trajectories had previously been considered as merely physical (rather than mathematical) phe nomena. A. N. Kolmogorov generalized Wiener's construction to allow one to establish the existence of a measure corresponding to an arbitrary random process. These investigations were the beginning of the development of the theory of stochastic processes. A considerable part of this theory involves the solution of problems in the theory of measures on function spaces in the specific language of stochastic pro cesses. For example, finding the properties of sample functions is connected with the problem of the existence of a measure on some space; certain problems in statisticsreduce to the calculation of the density of one measure w. r. t. another one, and the study of transformations of random processes leads to the study of transformations of function spaces with measure. One must note that the language of probability theory tends to obscure the results obtained in these areas for mathematicians working in other fields. Another dir,ection leading to the study of integrals in function space is the theory and application of differential equations. A. N.

Operator Theory For Complex And Hypercomplex Analysis

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Author : Enrique Ramírez de Arellano
language : en
Publisher: American Mathematical Soc.
Release Date : 1998

Operator Theory For Complex And Hypercomplex Analysis written by Enrique Ramírez de Arellano 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 1998 with Mathematics categories.

This book presents a collection of papers on certain aspects of general operator theory related to classes of important operators: singular integral, Toeplitz and Bergman opertors, convolution operators on Lie groups, pseudodifferential operators, etc. The study of these operators arises from integral representations for different classes of functions, enriches pure opertor theory, and is influential and beneficial for important areas of analysis. Particular attention is paid to the fruitful interplay of recent developments of complex and hypercomplex analysis on one side and to operator theory on the other. The majority of papers illustrate this interplay as well as related applications. The papers represent the proceedings of the conference "Operator Theory and Complex and Hypercomplex Analysis", held in Decenber 1994 in Mexico City.