Noncommutative Integration And Operator Theory

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Noncommutative Integration and Operator Theory

Author : Peter G. Dodds
Publisher : Springer Nature
ISBN 13 : 303149654X
Total Pages : 583 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Noncommutative Integration and Operator Theory by : Peter G. Dodds

Download or read book Noncommutative Integration and Operator Theory written by Peter G. Dodds and published by Springer Nature. This book was released on 2024-01-19 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this monograph is to provide a systematic account of the theory of noncommutative integration in semi-finite von Neumann algebras. It is designed to serve as an introductory graduate level text as well as a basic reference for more established mathematicians with interests in the continually expanding areas of noncommutative analysis and probability. Its origins lie in two apparently distinct areas of mathematical analysis: the theory of operator ideals going back to von Neumann and Schatten and the general theory of rearrangement invariant Banach lattices of measurable functions which has its roots in many areas of classical analysis related to the well-known Lp-spaces. A principal aim, therefore, is to present a general theory which contains each of these motivating areas as special cases.

Noncommutative Analysis, Operator Theory and Applications

Author : Daniel Alpay
Publisher : Birkhäuser
ISBN 13 : 3319291165
Total Pages : 283 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Noncommutative Analysis, Operator Theory and Applications by : Daniel Alpay

Download or read book Noncommutative Analysis, Operator Theory and Applications written by Daniel Alpay and published by Birkhäuser. This book was released on 2016-06-30 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book illustrates several aspects of the current research activity in operator theory, operator algebras and applications in various areas of mathematics and mathematical physics. It is addressed to specialists but also to graduate students in several fields including global analysis, Schur analysis, complex analysis, C*-algebras, noncommutative geometry, operator algebras, operator theory and their applications. Contributors: F. Arici, S. Bernstein, V. Bolotnikov, J. Bourgain, P. Cerejeiras, F. Cipriani, F. Colombo, F. D'Andrea, G. Dell'Antonio, M. Elin, U. Franz, D. Guido, T. Isola, A. Kula, L.E. Labuschagne, G. Landi, W.A. Majewski, I. Sabadini, J.-L. Sauvageot, D. Shoikhet, A. Skalski, H. de Snoo, D. C. Struppa, N. Vieira, D.V. Voiculescu, and H. Woracek.

Unbounded Non-Commutative Integration

Author : J.P. Jurzak
Publisher : Springer Science & Business Media
ISBN 13 : 9400952317
Total Pages : 209 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Unbounded Non-Commutative Integration by : J.P. Jurzak

Download or read book Unbounded Non-Commutative Integration written by J.P. Jurzak and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-commutative integration has its origin in the classical papers of Murray and von Neumann on rings of operators, and was introduced because of unsolved problems in unitary group representations and the elucidation of various aspects of quantum-mechanical formalism, together with formal calculus in such operator rings. These papers emphasized the interest in 1I -factors and pOinted out the remarkable behavior and 1 algebraic structure of the set of all unbounded closed operators a. ffiliated to such rings. The absence of power tools in functional analysis - mainly settled in their definitive form by A. Grothendieck around 1950-195- together with the pathological manipulation of algebraic operations on closed operators in Hilbert spaces, has limited ring-theory to the study of algebras of bounded operators with the main objective the difficult question of classifica tion up to isomorphisms of factors. This material has permitted a rigorous study of discrete systems in statistical mechanics but appears to be less convincing in other domains of physics (in the algebraic approach to field theory, for example). The striking role of Hamiltonians, Schrodinger operators and Lie group invariant properties in such areas of physics disappears in the so called C*-approach.

Theory of Operator Algebras I

Author : Masamichi Takesaki
Publisher : Springer Science & Business Media
ISBN 13 : 1461261880
Total Pages : 424 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Theory of Operator Algebras I by : Masamichi Takesaki

Download or read book Theory of Operator Algebras I written by Masamichi Takesaki and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics for infinite dimensional objects is becoming more and more important today both in theory and application. Rings of operators, renamed von Neumann algebras by J. Dixmier, were first introduced by J. von Neumann fifty years ago, 1929, in [254] with his grand aim of giving a sound founda tion to mathematical sciences of infinite nature. J. von Neumann and his collaborator F. J. Murray laid down the foundation for this new field of mathematics, operator algebras, in a series of papers, [240], [241], [242], [257] and [259], during the period of the 1930s and early in the 1940s. In the introduction to this series of investigations, they stated Their solution 1 {to the problems of understanding rings of operators) seems to be essential for the further advance of abstract operator theory in Hilbert space under several aspects. First, the formal calculus with operator-rings leads to them. Second, our attempts to generalize the theory of unitary group-representations essentially beyond their classical frame have always been blocked by the unsolved questions connected with these problems. Third, various aspects of the quantum mechanical formalism suggest strongly the elucidation of this subject. Fourth, the knowledge obtained in these investigations gives an approach to a class of abstract algebras without a finite basis, which seems to differ essentially from all types hitherto investigated. Since then there has appeared a large volume of literature, and a great deal of progress has been achieved by many mathematicians.

Noncommutative Geometry

Author : Alain Connes
Publisher : Springer Science & Business Media
ISBN 13 : 9783540203575
Total Pages : 372 pages
Book Rating : 4.2/5 (35 download)

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Book Synopsis Noncommutative Geometry by : Alain Connes

Download or read book Noncommutative Geometry written by Alain Connes and published by Springer Science & Business Media. This book was released on 2003-12-08 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.

Theory of Operator Algebras II

Author : Masamichi Takesaki
Publisher : Springer Science & Business Media
ISBN 13 : 9783540429142
Total Pages : 552 pages
Book Rating : 4.4/5 (291 download)

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Book Synopsis Theory of Operator Algebras II by : Masamichi Takesaki

Download or read book Theory of Operator Algebras II written by Masamichi Takesaki and published by Springer Science & Business Media. This book was released on 2002-11-01 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Together with Theory of Operator Algebras I and III, this book presents the theory of von Neumann algebras and non-commutative integration focusing on the group of automorphisms and the structure analysis. From the reviews: "These books can be warmly recommended to every graduate student who wants to become acquainted with this exciting branch of mathematics. Furthermore, they should be on the bookshelf of every researcher of the area." --ACTA SCIENTIARUM MATHEMATICARUM

Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology

Author : Raul E Curto
Publisher : Springer Nature
ISBN 13 : 3030433803
Total Pages : 531 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology by : Raul E Curto

Download or read book Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology written by Raul E Curto and published by Springer Nature. This book was released on 2020-12-12 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and noncommutative topology. Its goal is to give graduate students and researchers a relatively comprehensive overview of the current status of research in the relevant fields. The book is also a special volume dedicated to the memory of Ronald G. Douglas who passed away on February 27, 2018 at the age of 79. Many of the contributors are Douglas’ students and past collaborators. Their articles attest and commemorate his life-long contribution and influence to these fields.

Operator Theory on Noncommutative Domains

Author : Gelu Popescu
Publisher :
ISBN 13 : 9781470405786
Total Pages : 124 pages
Book Rating : 4.4/5 (57 download)

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Book Synopsis Operator Theory on Noncommutative Domains by : Gelu Popescu

Download or read book Operator Theory on Noncommutative Domains written by Gelu Popescu and published by . This book was released on 2010 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Noncommutative Function-Theoretic Operator Theory and Applications

Author : Joseph A. Ball
Publisher : Cambridge University Press
ISBN 13 : 1009020102
Total Pages : 440 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Noncommutative Function-Theoretic Operator Theory and Applications by : Joseph A. Ball

Download or read book Noncommutative Function-Theoretic Operator Theory and Applications written by Joseph A. Ball and published by Cambridge University Press. This book was released on 2021-12-16 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system theory ideas and reproducing kernel techniques, the book then covers representations of backward-shift-invariant subspaces in the Hardy space as ranges of observability operators, and representations for forward-shift-invariant subspaces via a Beurling–Lax representer equal to the transfer function of the linear system. This pair of backward-shift-invariant and forward-shift-invariant subspace form a generalized orthogonal decomposition of the ambient Hardy space. All this leads to the de Branges–Rovnyak model theory and characteristic operator function for a Hilbert space contraction operator. The chapters that follow generalize the system theory and reproducing kernel techniques to enable an extension of the ideas above to weighted Bergman space multivariable settings.

Vector Measures, Integration and Related Topics

Author : Guillermo Curbera
Publisher : Springer Science & Business Media
ISBN 13 : 3034602111
Total Pages : 382 pages
Book Rating : 4.0/5 (346 download)

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Book Synopsis Vector Measures, Integration and Related Topics by : Guillermo Curbera

Download or read book Vector Measures, Integration and Related Topics written by Guillermo Curbera and published by Springer Science & Business Media. This book was released on 2010-02-21 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of articles on the theme "vector measures, integration and applications" together with some related topics. The articles consist of both survey style and original research papers, are written by experts in thearea and present a succinct account of recent and up-to-date knowledge. The topic is interdisciplinary by nature and involves areas such as measure and integration (scalar, vector and operator-valued), classical and harmonic analysis, operator theory, non-commutative integration, andfunctional analysis. The material is of interest to experts, young researchers and postgraduate students.

Operator Algebras, Quantization, and Noncommutative Geometry

Author : John Von Neumann
Publisher : American Mathematical Soc.
ISBN 13 : 9780821856994
Total Pages : 436 pages
Book Rating : 4.8/5 (569 download)

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Book Synopsis Operator Algebras, Quantization, and Noncommutative Geometry by : John Von Neumann

Download or read book Operator Algebras, Quantization, and Noncommutative Geometry written by John Von Neumann and published by American Mathematical Soc.. This book was released on 2004 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: John von Neumann and Marshall Stone were two giants of Twentieth Century mathematics. In honor of the 100th anniversary of their births, a mathematical celebration was organized featuring developments in fields where both men were major influences. This volume contains articles from the AMS Special Session, Operator Algebras, Quantization and Noncommutative Geometry: A Centennial Celebration in Honor of John von Neumann and Marshall H. Stone. Papers range from expository and historical surveys to original research articles. All articles were carefully refereed and cover a broad range of mathematical topics reflecting the fundamental ideas of von Neumann and Stone. The book is suitable for graduate students and researchers interested in operator algebras and applications, including noncommutative geometry.

Operator Theory in Harmonic and Non-commutative Analysis

Author : Joseph A. Ball
Publisher : Springer
ISBN 13 : 3319062662
Total Pages : 256 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Operator Theory in Harmonic and Non-commutative Analysis by : Joseph A. Ball

Download or read book Operator Theory in Harmonic and Non-commutative Analysis written by Joseph A. Ball and published by Springer. This book was released on 2014-06-21 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the 23rd International Workshop on Operator Theory and its Applications (IWOTA 2012), which was held at the University of New South Wales (Sydney, Australia) from 16 July to 20 July 2012. It includes twelve articles presenting both surveys of current research in operator theory and original results.

Theory of Operator Algebras II

Author : Masamichi Takesaki
Publisher : Springer
ISBN 13 : 9783540429142
Total Pages : 518 pages
Book Rating : 4.4/5 (291 download)

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Book Synopsis Theory of Operator Algebras II by : Masamichi Takesaki

Download or read book Theory of Operator Algebras II written by Masamichi Takesaki and published by Springer. This book was released on 2002-11-01 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Together with Theory of Operator Algebras I and III, this book presents the theory of von Neumann algebras and non-commutative integration focusing on the group of automorphisms and the structure analysis. From the reviews: "These books can be warmly recommended to every graduate student who wants to become acquainted with this exciting branch of mathematics. Furthermore, they should be on the bookshelf of every researcher of the area." --ACTA SCIENTIARUM MATHEMATICARUM

Multilinear Operator Integrals

Author : Anna Skripka
Publisher : Springer Nature
ISBN 13 : 3030324060
Total Pages : 192 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Multilinear Operator Integrals by : Anna Skripka

Download or read book Multilinear Operator Integrals written by Anna Skripka and published by Springer Nature. This book was released on 2019-12-01 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive treatment of multilinear operator integral techniques. The exposition is structured to be suitable for a course on methods and applications of multilinear operator integrals and also as a research aid. The ideas and contributions to the field are surveyed and up-to-date results and methods are presented. Most practical constructions of multiple operator integrals are included along with fundamental technical results and major applications to smoothness properties of operator functions (Lipschitz and Hölder continuity, differentiability), approximation of operator functions, spectral shift functions, spectral flow in the setting of noncommutative geometry, quantum differentiability, and differentiability of noncommutative L^p-norms. Main ideas are demonstrated in simpler cases, while more involved, technical proofs are outlined and supplemented with references. Selected open problems in the field are also presented.

Integrals and Operators

Author : I.E. Segal
Publisher : Springer Science & Business Media
ISBN 13 : 3642666930
Total Pages : 387 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Integrals and Operators by : I.E. Segal

Download or read book Integrals and Operators written by I.E. Segal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: TO THE SECOND EDITION Since publication of the First Edition several excellent treatments of advanced topics in analysis have appeared. However, the concentration and penetration of these treatises naturally require much in the way of technical preliminaries and new terminology and notation. There consequently remains a need for an introduction to some of these topics which would mesh with the material of the First Edition. Such an introduction could serve to exemplify the material further, while using it to shorten and simplify its presentation. It seemed particularly important as well as practical to treat briefly but cogently some of the central parts of operator algebra and higher operator theory, as these are presently represented in book form only with a degree of specialization rather beyond the immediate needs or interests of many readers. Semigroup and perturbation theory provide connections with the theory of partial differential equations. C*-algebras are important in har monic analysis and the mathematical foundations of quantum mechanics. W*-algebras (or von Neumann rings) provide an approach to the theory of multiplicity of the spectrum and some simple but key elements of the gram mar of analysis, of use in group representation theory and elsewhere. The v vi Preface to the Second Edition theory of the trace for operators on Hilbert space is both important in itself and a natural extension of earlier integration-theoretic ideas.

Theory

Author : Steven Lord
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110392313
Total Pages : 304 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis Theory by : Steven Lord

Download or read book Theory written by Steven Lord and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-07-19 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second edition of the first complete study and monograph dedicated to singular traces. The text offers, due to the contributions of Albrecht Pietsch and Nigel Kalton, a complete theory of traces and their spectral properties on ideals of compact operators on a separable Hilbert space. The second edition has been updated on the fundamental approach provided by Albrecht Pietsch. For mathematical physicists and other users of Connes’ noncommutative geometry the text offers a complete reference to traces on weak trace class operators, including Dixmier traces and associated formulas involving residues of spectral zeta functions and asymptotics of partition functions.

Operator Algebras, Operator Theory and Applications

Author : J. J. Grobler
Publisher : Springer Science & Business Media
ISBN 13 : 3034601743
Total Pages : 294 pages
Book Rating : 4.0/5 (346 download)

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Book Synopsis Operator Algebras, Operator Theory and Applications by : J. J. Grobler

Download or read book Operator Algebras, Operator Theory and Applications written by J. J. Grobler and published by Springer Science & Business Media. This book was released on 2009-12-24 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the eighteenth International Workshop on Operator Theory and Applications (IWOTA), hosted by the Unit for Business Mathematics and Informatics of North-West University, Potchefstroom, South Africa from July 3 to 6, 2007. The conference (as well as these proceedings) was dedicated to Professors Joseph A. Ball and Marinus M. Kaashoek on the occasion of their 60th and 70th birthdays, respectively. This conference had a particular focus on Von Neumann algebras at the interface of operator theory with functional analysis and on applications of operator theory to differential equations.