Commutation Properties Of Hilbert Space Operators

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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

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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.

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.

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.

Operators On Hilbert Space

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Author : V. S. Sunder
language : en
Publisher: Springer
Release Date : 2016-08-05

Operators On Hilbert Space written by V. S. Sunder and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-05 with Mathematics categories.

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.

Introduction To Spectral Theory In Hilbert Space

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Author : Gilbert Helmberg
language : en
Publisher: Elsevier
Release Date : 2014-11-28

Introduction To Spectral Theory In Hilbert Space written by Gilbert Helmberg and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-28 with Science categories.

North-Holland Series in Applied Mathematics and Mechanics, Volume 6: Introduction to Spectral Theory in Hilbert Space focuses on the mechanics, principles, and approaches involved in spectral theory in Hilbert space. The publication first elaborates on the concept and specific geometry of Hilbert space and bounded linear operators. Discussions focus on projection and adjoint operators, bilinear forms, bounded linear mappings, isomorphisms, orthogonal subspaces, base, subspaces, finite dimensional Euclidean space, and normed linear spaces. The text then takes a look at the general theory of linear operators and spectral analysis of compact linear operators, including spectral decomposition of a compact selfadjoint operator, weakly convergent sequences, spectrum of a compact linear operator, and eigenvalues of a linear operator. The manuscript ponders on the spectral analysis of bounded linear operators and unbounded selfadjoint operators. Topics include spectral decomposition of an unbounded selfadjoint operator and bounded normal operator, functions of a unitary operator, step functions of a bounded selfadjoint operator, polynomials in a bounded operator, and order relation for bounded selfadjoint operators. The publication is a valuable source of data for mathematicians and researchers interested in spectral theory in Hilbert space.

Product And Commutation Properties Of Hilbert Space Operators

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Author : Michael John Hoffman
language : en
Publisher:
Release Date : 1979

Product And Commutation Properties Of Hilbert Space Operators written by Michael John Hoffman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with categories.

Approximation Of Hilbert Space Operators

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Author : Domingo A. Herrero
language : en
Publisher: Pitman Advanced Publishing Program
Release Date : 1982

Approximation Of Hilbert Space Operators written by Domingo A. Herrero and has been published by Pitman Advanced Publishing Program this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.

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.

C0 Groups Commutator Methods And Spectral Theory Of N Body Hamiltonians

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Author : Werner O. Amrein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-26

C0 Groups Commutator Methods And Spectral Theory Of N Body Hamiltonians written by Werner O. Amrein 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 2013-11-26 with Mathematics categories.

The conjugate operator method is a powerful recently developed technique for studying spectral properties of self-adjoint operators. One of the purposes of this volume is to present a refinement of the original method due to Mourre leading to essentially optimal results in situations as varied as ordinary differential operators, pseudo-differential operators and N-body Schrödinger hamiltonians. Another topic is a new algebraic framework for the N-body problem allowing a simple and systematic treatment of large classes of many-channel hamiltonians. The monograph will be of interest to research mathematicians and mathematical physicists. The authors have made efforts to produce an essentially self-contained text, which makes it accessible to advanced students. Thus about one third of the book is devoted to the development of tools from functional analysis, in particular real interpolation theory for Banach spaces and functional calculus and Besov spaces associated with multi-parameter C0-groups. Certainly this monograph (containing a bibliography of 170 items) is a well-written contribution to this field which is suitable to stimulate further evolution of the theory. (Mathematical Reviews)