Operator Algebras In Dynamical Systems

Author : Shōichirō Sakai
Publisher : Cambridge University Press
ISBN 13 : 0521400961
Total Pages : 235 pages
Book Rating : 4.61/5 ( download)

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Download or read book Operator Algebras in Dynamical Systems written by Shōichirō Sakai and published by Cambridge University Press. This book was released on 1991-08-30 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the theory of unbounded derivations in C*-algebras, a subject whose study was motivated by questions in quantum physics and statistical mechanics, and to which the author has made a considerable contribution. This is an active area of research, and one of the most ambitious aims of the theory is to develop quantum statistical mechanics within the framework of the C*-theory. The presentation, which is based on lectures given in Newcastle upon Tyne and Copenhagen, concentrates on topics involving quantum statistical mechanics and differentiations on manifolds. One of the goals is to formulate the absence theorem of phase transitions in its most general form within the C* setting. For the first time, he globally constructs, within that setting, derivations for a fairly wide class of interacting models, and presents a new axiomatic treatment of the construction of time evolutions and KMS states.

Author : Sergey Neshveyev
Publisher : Springer Science & Business Media
ISBN 13 : 3540346732
Total Pages : 294 pages
Book Rating : 4.39/5 ( download)

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Download or read book Dynamical Entropy in Operator Algebras written by Sergey Neshveyev and published by Springer Science & Business Media. This book was released on 2006-09-22 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book addresses mathematicians and physicists, including graduate students, who are interested in quantum dynamical systems and applications of operator algebras and ergodic theory. It is the only monograph on this topic. Although the authors assume a basic knowledge of operator algebras, they give precise definitions of the notions and in most cases complete proofs of the results which are used.

Author : Shtichirt Sakai
Publisher :
ISBN 13 : 9781107094451
Total Pages : 233 pages
Book Rating : 4.53/5 ( download)

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Download or read book Operator Algebras in Dynamical Systems written by Shtichirt Sakai and published by . This book was released on 2014-05-18 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is essential reading for graduate students and professionals working in operator algebras, mathematical physics and functional analysis.

Author : Shôichirô Sakai
Publisher :
ISBN 13 : 9781107088238
Total Pages : 233 pages
Book Rating : 4.32/5 ( download)

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Download or read book Operator Algebras in Dynamical Systems written by Shôichirô Sakai and published by . This book was released on 2014-05-14 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is essential reading for graduate students and professionals working in operator algebras, mathematical physics and functional analysis.

Author : Hari Bercovici
Publisher : CRC Press
ISBN 13 : 1351643037
Total Pages : 219 pages
Book Rating : 4.30/5 ( download)

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Download or read book Recent Advances in Operator Theory and Operator Algebras written by Hari Bercovici and published by CRC Press. This book was released on 2017-08-07 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will contain lectures given by four eminent speakers at the Recent Advances in Operator Theory and Operator Algebras conference held at the Indian Statistical Institute, Bangalore, India in 2014. The main aim of this book is to bring together various results in one place with cogent introduction and references for further study.

Author : Kenneth R. Davidson
Publisher : American Mathematical Soc.
ISBN 13 : 0821853023
Total Pages : 68 pages
Book Rating : 4.23/5 ( download)

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Download or read book Operator Algebras for Multivariable Dynamics written by Kenneth R. Davidson and published by American Mathematical Soc.. This book was released on 2011 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\sigma_i:X \to X$ for $1 \le i \le n$. To this the authors associate two conjugacy operator algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra $\mathcal{A}(X,\tau)$ and the semicrossed product $\mathrm{C}_0(X)\times_\tau\mathbb{F}_n^+$. They develop the necessary dilation theory for both models. In particular, they exhibit an explicit family of boundary representations which determine the C*-envelope of the tensor algebra.|Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\sigma_i:X \to X$ for $1 \le i \le n$. To this the authors associate two conjugacy operator algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra $\mathcal{A}(X,\tau)$ and the semicrossed product $\mathrm{C}_0(X)\times_\tau\mathbb{F}_n^+$. They develop the necessary dilation theory for both models. In particular, they exhibit an explicit family of boundary representations which determine the C*-envelope of the tensor algebra.

Author : Toke M. Carlsen
Publisher : Springer
ISBN 13 : 9783642394607
Total Pages : 332 pages
Book Rating : 4.04/5 ( download)

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Download or read book Operator Algebra and Dynamics written by Toke M. Carlsen and published by Springer. This book was released on 2013-12-06 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on presentations given at the NordForsk Network Closing Conference “Operator Algebra and Dynamics,” held in Gjáargarður, Faroe Islands, in May 2012, this book features high quality research contributions and review articles by researchers associated with the NordForsk network and leading experts that explore the fundamental role of operator algebras and dynamical systems in mathematics with possible applications to physics, engineering and computer science. It covers the following topics: von Neumann algebras arising from discrete measured groupoids, purely infinite Cuntz-Krieger algebras, filtered K-theory over finite topological spaces, C*-algebras associated to shift spaces (or subshifts), graph C*-algebras, irrational extended rotation algebras that are shown to be C*-alloys, free probability, renewal systems, the Grothendieck Theorem for jointly completely bounded bilinear forms on C*-algebras, Cuntz-Li algebras associated with the a-adic numbers, crossed products of injective endomorphisms (the so-called Stacey crossed products), the interplay between dynamical systems, operator algebras and wavelets on fractals, C*-completions of the Hecke algebra of a Hecke pair, semiprojective C*-algebras, and the topological dimension of type I C*-algebras. Operator Algebra and Dynamics will serve as a useful resource for a broad spectrum of researchers and students in mathematics, physics, and engineering.

Author : Shōichirō Sakai
Publisher : Cambridge University Press
ISBN 13 : 9780521060219
Total Pages : 232 pages
Book Rating : 4.14/5 ( download)

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Download or read book Operator Algebras in Dynamical Systems written by Shōichirō Sakai and published by Cambridge University Press. This book was released on 2008-02-04 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the theory of unbounded derivations in C*-algebras, a subject whose study was motivated by questions in quantum physics and statistical mechanics, and to which the author has made considerable contributions. This is an active area of research, and one of the most ambitious aims of the theory is to develop quantum statistical mechanics within the framework of C*-theory. The presentation concentrates on topics involving quantum statistical mechanics and differentiations on manifolds. One of the goals is to formulate the absence theorem of phase transitions in its most general form within the C* setting. For the first time, the author globally constructs, within that setting, derivations for a fairly wide class of interacting models, and presents a new axiomatic treatment of the construction of time evolutions and KMS states.

Author : Marcel de Jeu
Publisher : American Mathematical Soc.
ISBN 13 : 0821847473
Total Pages : 329 pages
Book Rating : 4.73/5 ( download)

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Download or read book Operator Structures and Dynamical Systems written by Marcel de Jeu and published by American Mathematical Soc.. This book was released on 2009-11-30 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of a Leiden Workshop on Dynamical Systems and their accompanying Operator Structures which took place at the Lorentz Center in Leiden, The Netherlands, on July 21-25, 2008. These papers offer a panorama of selfadjoint and non-selfadjoint operator algebras associated with both noncommutative and commutative (topological) dynamical systems and related subjects. Papers on general theory, as well as more specialized ones on symbolic dynamics and complex dynamical systems, are included.

Author : Toke M. Carlsen
Publisher : Springer Science & Business Media
ISBN 13 : 3642394590
Total Pages : 343 pages
Book Rating : 4.91/5 ( download)

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Download or read book Operator Algebra and Dynamics written by Toke M. Carlsen and published by Springer Science & Business Media. This book was released on 2013-12-03 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on presentations given at the NordForsk Network Closing Conference “Operator Algebra and Dynamics,” held in Gjáargarður, Faroe Islands, in May 2012, this book features high quality research contributions and review articles by researchers associated with the NordForsk network and leading experts that explore the fundamental role of operator algebras and dynamical systems in mathematics with possible applications to physics, engineering and computer science. It covers the following topics: von Neumann algebras arising from discrete measured groupoids, purely infinite Cuntz-Krieger algebras, filtered K-theory over finite topological spaces, C*-algebras associated to shift spaces (or subshifts), graph C*-algebras, irrational extended rotation algebras that are shown to be C*-alloys, free probability, renewal systems, the Grothendieck Theorem for jointly completely bounded bilinear forms on C*-algebras, Cuntz-Li algebras associated with the a-adic numbers, crossed products of injective endomorphisms (the so-called Stacey crossed products), the interplay between dynamical systems, operator algebras and wavelets on fractals, C*-completions of the Hecke algebra of a Hecke pair, semiprojective C*-algebras, and the topological dimension of type I C*-algebras. Operator Algebra and Dynamics will serve as a useful resource for a broad spectrum of researchers and students in mathematics, physics, and engineering.