Dynamical Entropy In Operator Algebras

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 : 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 : M. Rordam
Publisher : Springer Science & Business Media
ISBN 13 : 3662048256
Total Pages : 206 pages
Book Rating : 4.52/5 ( download)

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Download or read book Classification of Nuclear C*-Algebras. Entropy in Operator Algebras written by M. Rordam and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: to the Encyclopaedia Subseries on Operator Algebras and Non-Commutative Geometry The theory of von Neumann algebras was initiated in a series of papers by Murray and von Neumann in the 1930's and 1940's. A von Neumann algebra is a self-adjoint unital subalgebra M of the algebra of bounded operators of a Hilbert space which is closed in the weak operator topology. According to von Neumann's bicommutant theorem, M is closed in the weak operator topology if and only if it is equal to the commutant of its commutant. Afactor is a von Neumann algebra with trivial centre and the work of Murray and von Neumann contained a reduction of all von Neumann algebras to factors and a classification of factors into types I, II and III. C* -algebras are self-adjoint operator algebras on Hilbert space which are closed in the norm topology. Their study was begun in the work of Gelfand and Naimark who showed that such algebras can be characterized abstractly as involutive Banach algebras, satisfying an algebraic relation connecting the norm and the involution. They also obtained the fundamental result that a commutative unital C* -algebra is isomorphic to the algebra of complex valued continuous functions on a compact space - its spectrum. Since then the subject of operator algebras has evolved into a huge mathematical endeavour interacting with almost every branch of mathematics and several areas of theoretical physics.

Author : Dan V. Voiculescu
Publisher :
ISBN 13 :
Total Pages : 31 pages
Book Rating : 4.23/5 ( download)

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Download or read book Dynamical Approximation Entropies and Topological Entropy in Operator Algebras written by Dan V. Voiculescu and published by . This book was released on 1994 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : M. Ohya
Publisher : Springer Science & Business Media
ISBN 13 : 9783540208068
Total Pages : 368 pages
Book Rating : 4.62/5 ( download)

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Download or read book Quantum Entropy and Its Use written by M. Ohya and published by Springer Science & Business Media. This book was released on 2004-03-24 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerous fundamental properties of quantum information measurement are developed, including the von Neumann entropy of a statistical operator and its limiting normalized version, the entropy rate. Use of quantum-entropy quantities is made in perturbation theory, central limit theorems, thermodynamics of spin systems, entropic uncertainty relations, and optical communication. This new softcover corrected reprint contains summaries of recent developments added to the ends of the chapters.

Author : Institut des hautes études scientifiques (Paris, France)
Publisher : American Mathematical Soc.
ISBN 13 : 0821852035
Total Pages : 695 pages
Book Rating : 4.33/5 ( download)

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Download or read book Quanta of Maths written by Institut des hautes études scientifiques (Paris, France) and published by American Mathematical Soc.. This book was released on 2010 with total page 695 pages. Available in PDF, EPUB and Kindle. Book excerpt: The work of Alain Connes has cut a wide swath across several areas of mathematics and physics. Reflecting its broad spectrum and profound impact on the contemporary mathematical landscape, this collection of articles covers a wealth of topics at the forefront of research in operator algebras, analysis, noncommutative geometry, topology, number theory and physics. Specific themes covered by the articles are as follows: entropy in operator algebras, regular $C^*$-algebras of integral domains, properly infinite $C^*$-algebras, representations of free groups and 1-cohomology, Leibniz seminorms and quantum metric spaces; von Neumann algebras, fundamental Group of $\mathrm{II}_1$ factors, subfactors and planar algebras; Baum-Connes conjecture and property T, equivariant K-homology, Hermitian K-theory; cyclic cohomology, local index formula and twisted spectral triples, tangent groupoid and the index theorem; noncommutative geometry and space-time, spectral action principle, quantum gravity, noncommutative ADHM and instantons, non-compact spectral triples of finite volume, noncommutative coordinate algebras; Hopf algebras, Vinberg algebras, renormalization and combinatorics, motivic renormalization and singularities; cyclotomy and analytic geometry over $F_1$, quantum modular forms; differential K-theory, cyclic theory and S-cohomology.

Author : Masanori Ohya
Publisher : World Scientific
ISBN 13 : 9812794204
Total Pages : 489 pages
Book Rating : 4.08/5 ( download)

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Download or read book Selected Papers of M. Ohya written by Masanori Ohya and published by World Scientific. This book was released on 2008 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of articles written by Professor M Ohya over the past three decades in the areas of quantum teleportation, quantum information theory, quantum computer, etc. By compiling Ohya''s important works in these areas, the book serves as a useful reference for researchers who are working in these fields. Sample Chapter(s). Introduction (109 KB). Chapter 1: Adaptive Dynamics and Its Applications To Chaos and Npc Problem (1,633 KB). Contents: Adaptive Dynamics and Its Applications; A Stochastic Limit Approach to the SAT Problem; Quantum Algorithm for SAT Problem and Quantum Mutual Entropy; NP Problem in Quantum Algorithm; New Quantum Algorithm for Studying NP-complete Problems; Quantum Teleportation and Beam Splitting; Entanglement, Quantum Entropy and Mutual Information; Quantum Dynamical Entropy for Completely Positive Maps; On Capacities of Quantum Channels; Compound Channels, Transition Expectations, and Liftings; Information Dynamics and Its Application to Optical Communication Processes; Complexity and Fractal Dimension for Quantum States; Information Theoretical Treatment of Genes; Some Aspects of Quantum Information Theory and Their Applications to Irreversible Processes; On Compound State and Mutual Information in Quantum Information Theory; Quantum Ergodic Channels in Operator Algebras; and others papers. Readership: Researchers in quantum entropy, quantum information theory and mathematical physics.

Author : Robert S. Doran
Publisher : American Mathematical Soc.
ISBN 13 : 1470419483
Total Pages : 282 pages
Book Rating : 4.86/5 ( download)

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Download or read book Operator Algebras and Their Applications written by Robert S. Doran and published by American Mathematical Soc.. This book was released on 2016-07-28 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: his volume contains the proceedings of the AMS Special Session Operator Algebras and Their Applications: A Tribute to Richard V. Kadison, held from January 10–11, 2015, in San Antonio, Texas. Richard V. Kadison has been a towering figure in the study of operator algebras for more than 65 years. His research and leadership in the field have been fundamental in the development of the subject, and his influence continues to be felt though his work and the work of his many students, collaborators, and mentees. Among the topics addressed in this volume are the Kadison-Kaplanksy conjecture, classification of C∗-algebras, connections between operator spaces and parabolic induction, spectral flow, C∗-algebra actions, von Neumann algebras, and applications to mathematical physics.

Author : Erling Størmer
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.71/5 ( download)

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Download or read book Entropy in operator algebras written by Erling Størmer and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Ola Bratteli
Publisher : Springer Science & Business Media
ISBN 13 :
Total Pages : 544 pages
Book Rating : 4.57/5 ( download)

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Download or read book Operator Algebras and Quantum Statistical Mechanics written by Ola Bratteli and published by Springer Science & Business Media. This book was released on 1979 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.