Noncommutative Integration And Operator Theory

Author : Peter G. Dodds,Ben de Pagter,Fedor A. Sukochev
Publisher : Springer Nature
Page : 583 pages
File Size : 46,5 Mb
Release : 2024-01-19
Category : Mathematics
ISBN : 9783031496547

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Noncommutative Integration and Operator Theory by Peter G. Dodds,Ben de Pagter,Fedor A. Sukochev Pdf

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.

Author : J.P. Jurzak
Publisher : Springer Science & Business Media
Page : 209 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400952317

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Unbounded Non-Commutative Integration by J.P. Jurzak Pdf

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.

Author : Daniel Alpay,Fabio Cipriani,Fabrizio Colombo,Daniele Guido,Irene Sabadini,Jean-Luc Sauvageot
Publisher : Birkhäuser
Page : 283 pages
File Size : 41,9 Mb
Release : 2016-06-30
Category : Mathematics
ISBN : 9783319291161

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Noncommutative Analysis, Operator Theory and Applications by Daniel Alpay,Fabio Cipriani,Fabrizio Colombo,Daniele Guido,Irene Sabadini,Jean-Luc Sauvageot Pdf

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.

Author : Masamichi Takesaki
Publisher : Springer Science & Business Media
Page : 537 pages
File Size : 40,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662104514

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Theory of Operator Algebras II by Masamichi Takesaki Pdf

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

Author : Masamichi Takesaki
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 54,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461261889

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Theory of Operator Algebras I by Masamichi Takesaki Pdf

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.

Author : Raul E Curto,William Helton,Huaxin Lin,Xiang Tang,Rongwei Yang,Guoliang Yu
Publisher : Springer Nature
Page : 531 pages
File Size : 45,9 Mb
Release : 2020-12-12
Category : Mathematics
ISBN : 9783030433802

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Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology by Raul E Curto,William Helton,Huaxin Lin,Xiang Tang,Rongwei Yang,Guoliang Yu Pdf

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.

Author : Jorgensen Palle,Tian Feng
Publisher : World Scientific
Page : 564 pages
File Size : 50,5 Mb
Release : 2017-01-24
Category : Mathematics
ISBN : 9789813202146

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Non-commutative Analysis by Jorgensen Palle,Tian Feng Pdf

The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret "non-commutative analysis" broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.) A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras. The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.

Author : Guillermo Curbera,Gerd Mockenhaupt,Werner J. Ricker
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 45,9 Mb
Release : 2010-02-21
Category : Mathematics
ISBN : 9783034602112

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Vector Measures, Integration and Related Topics by Guillermo Curbera,Gerd Mockenhaupt,Werner J. Ricker Pdf

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.

Author : Joseph A. Ball,Michael A. Dritschel,A.F.M. ter Elst,Pierre Portal,Denis Potapov
Publisher : Springer
Page : 260 pages
File Size : 40,9 Mb
Release : 2014-06-21
Category : Mathematics
ISBN : 9783319062662

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Operator Theory in Harmonic and Non-commutative Analysis by Joseph A. Ball,Michael A. Dritschel,A.F.M. ter Elst,Pierre Portal,Denis Potapov Pdf

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.

Author : Gelu Popescu
Publisher : Unknown
Page : 124 pages
File Size : 55,7 Mb
Release : 2010
Category : MATHEMATICS
ISBN : 1470405784

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Operator Theory on Noncommutative Domains by Gelu Popescu Pdf

Author : Masamichi Takesaki
Publisher : Springer
Page : 518 pages
File Size : 51,6 Mb
Release : 2002-11-01
Category : Mathematics
ISBN : 354042914X

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Theory of Operator Algebras II by Masamichi Takesaki Pdf

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

Author : Anna Skripka,Anna Tomskova
Publisher : Springer Nature
Page : 192 pages
File Size : 55,8 Mb
Release : 2019-12-01
Category : Mathematics
ISBN : 9783030324063

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Multilinear Operator Integrals by Anna Skripka,Anna Tomskova Pdf

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.

Author : Markus Haase
Publisher : Springer Science & Business Media
Page : 399 pages
File Size : 54,9 Mb
Release : 2006-08-18
Category : Mathematics
ISBN : 9783764376987

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The Functional Calculus for Sectorial Operators by Markus Haase Pdf

This book contains a systematic and partly axiomatic treatment of the holomorphic functional calculus for unbounded sectorial operators. The account is generic so that it can be used to construct and interrelate holomorphic functional calculi for other types of unbounded operators. Particularly, an elegant unified approach to holomorphic semigroups is obtained. The last chapter describes applications to PDE, evolution equations and approximation theory as well as the connection with harmonic analysis.

Author : Steven Lord,Fedor Sukochev,Dmitriy Zanin
Publisher : Walter de Gruyter GmbH & Co KG
Page : 304 pages
File Size : 50,8 Mb
Release : 2021-07-19
Category : Mathematics
ISBN : 9783110392319

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Theory by Steven Lord,Fedor Sukochev,Dmitriy Zanin Pdf

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.

Author : Joseph A. Ball,Vladimir Bolotnikov
Publisher : Cambridge University Press
Page : 439 pages
File Size : 45,8 Mb
Release : 2021-12-16
Category : Mathematics
ISBN : 9781316518991

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Noncommutative Function-Theoretic Operator Theory and Applications by Joseph A. Ball,Vladimir Bolotnikov Pdf

This concise volume shows how ideas from function and systems theory lead to new insights for noncommutative multivariable operator theory.