Symbolic Dynamical Systems And C Algebras

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Symbolic Dynamical Systems And C Algebras

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Author : Kengo Matsumoto
language : en
Publisher: Springer Nature
Release Date : 2025-02-06

Symbolic Dynamical Systems And C Algebras written by Kengo Matsumoto and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-06 with Mathematics categories.

This book presents the interplay between topological Markov shifts and Cuntz–Krieger algebras by providing notations, techniques, and ideas in detail. The main goal of this book is to provide a detailed proof of a classification theorem for continuous orbit equivalence of one-sided topological Markov shifts. The continuous orbit equivalence of one-sided topological Markov shifts is classified in terms of several different mathematical objects: the étale groupoids, the actions of the continuous full groups on the Markov shifts, the algebraic type of continuous full groups, the Cuntz–Krieger algebras, and the K-theory dates of the Cuntz–Krieger algebras. This classification result shows that topological Markov shifts have deep connections with not only operator algebras but also groupoid theory, infinite non-amenable groups, group actions, graph theory, linear algebras, K-theory, and so on. By using this classification result, the complete classification of flow equivalence in two-sided topological Markov shifts is described in terms of Cuntz–Krieger algebras. The author will also study the relationship between the topological conjugacy of topological Markov shifts and the gauge actions of Cuntz–Krieger algebras.

Operator Structures And Dynamical Systems

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Author : Marcel de Jeu
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-11-30

Operator Structures And Dynamical Systems written by Marcel de Jeu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-30 with Mathematics categories.

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.

Operator Algebra And Dynamics

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Author : Toke M. Carlsen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-03

Operator Algebra And Dynamics written by Toke M. Carlsen 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 2013-12-03 with Mathematics categories.

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.

Advances In Functional Analysis And Operator Theory

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Author : Marat V. Markin
language : en
Publisher: American Mathematical Society
Release Date : 2024-04-09

Advances In Functional Analysis And Operator Theory written by Marat V. Markin and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-09 with Mathematics categories.

This volume contains the proceedings of the AMS-EMS-SMF Special Session on Advances in Functional Analysis and Operator Theory, held July 18–22, 2022, at the Université de Grenoble-Alpes, Grenoble, France. The papers reflect the modern interplay between differential equations, functional analysis, operator algebras, and their applications from the dynamics to quantum groups to number theory. Among the topics discussed are the Sturm-Liouville and boundary value problems, axioms of quantum mechanics, $C^{*}$-algebras and symbolic dynamics, von Neumann algebras and low-dimensional topology, quantum permutation groups, the Jordan algebras, and the Kadison–Singer transforms.

Structural Analysis Of Complex Networks

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Author : Matthias Dehmer
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-14

Structural Analysis Of Complex Networks written by Matthias Dehmer 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 2010-10-14 with Mathematics categories.

Because of the increasing complexity and growth of real-world networks, their analysis by using classical graph-theoretic methods is oftentimes a difficult procedure. As a result, there is a strong need to combine graph-theoretic methods with mathematical techniques from other scientific disciplines, such as machine learning and information theory, in order to analyze complex networks more adequately. Filling a gap in literature, this self-contained book presents theoretical and application-oriented results to structurally explore complex networks. The work focuses not only on classical graph-theoretic methods, but also demonstrates the usefulness of structural graph theory as a tool for solving interdisciplinary problems. Special emphasis is given to methods related to: applications in biology, chemistry, linguistics, and data analysis; graph colorings; graph polynomials; information measures for graphs; metrical properties of graphs; partitions and decompositions; and quantitative graph measures. Structural Analysis of Complex Networks is suitable for a broad, interdisciplinary readership of researchers, practitioners, and graduate students in discrete mathematics, statistics, computer science, machine learning, artificial intelligence, computational and systems biology, cognitive science, computational linguistics, and mathematical chemistry. The book may be used as a supplementary textbook in graduate-level seminars on structural graph analysis, complex networks, or network-based machine learning methods.

C Algebras Of Homoclinic And Heteroclinic Structure In Expansive Dynamics

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Author : Klaus Thomsen
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-06-11

C Algebras Of Homoclinic And Heteroclinic Structure In Expansive Dynamics written by Klaus Thomsen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-11 with Mathematics categories.

The author unifies various constructions of $C^*$-algebras from dynamical systems, specifically, the dimension group construction of Krieger for shift spaces, the corresponding constructions of Wagoner and Boyle, Fiebig and Fiebig for countable state Markov shifts and one-sided shift spaces, respectively, and the constructions of Ruelle and Putnam for Smale spaces. The general setup is used to analyze the structure of the $C^*$-algebras arising from the homoclinic and heteroclinic equivalence relations in expansive dynamical systems, in particular, expansive group endomorphisms and automorphisms and generalized 1-solenoids. For these dynamical systems it is shown that the $C^*$-algebras are inductive limits of homogeneous or sub-homogeneous algebras with one-dimensional spectra.

Selected Papers On Analysis And Differential Equations

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Author : 野水克己
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

Selected Papers On Analysis And Differential Equations written by 野水克己 and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

This volume contains translations of papers that originally appeared in the Japanese journal, Sugaku. Ordinarily the papers would appear in the AMS translation of that journal, but to expedite publication, the Society has chosen to publish them as a volume of selected papers. The papers range over a variety of topics, including nonlinear partial differential equations, $C*$-algebras, and Schrodinger operators. The volume is suitable for graduate students and research mathematicians interested in analysis and differential equations.

Topics In Symbolic Dynamics And Applications

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Author : F. Blanchard
language : en
Publisher: Cambridge University Press
Release Date : 2000-06-29

Topics In Symbolic Dynamics And Applications written by F. Blanchard and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-29 with Mathematics categories.

This book is devoted to recent developments in symbolic dynamics, and it comprises eight chapters. The first two are concerned with the study of symbolic sequences of 'low complexity', the following two introduce 'high complexity' systems. The later chapters go on to deal with more specialised topics including ergodic theory, number theory, and one-dimensional dynamics.

Classification Of Nuclear C Algebras Entropy In Operator Algebras

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Author : M. Rordam
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18

Classification Of Nuclear C Algebras Entropy In Operator Algebras written by M. Rordam 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 2013-04-18 with Mathematics categories.

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.

Symbolic Dynamical Systems And C Algebras

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Author : Kengo Matsumoto
language : en
Publisher:
Release Date : 2025

Symbolic Dynamical Systems And C Algebras written by Kengo Matsumoto and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025 with Dynamics categories.

This book presents the interplay between topological Markov shifts and Cuntz-Krieger algebras by providing notations, techniques, and ideas in detail. The main goal of this book is to provide a detailed proof of a classification theorem for continuous orbit equivalence of one-sided topological Markov shifts. The continuous orbit equivalence of one-sided topological Markov shifts is classified in terms of several different mathematical objects: the étale groupoids, the actions of the continuous full groups on the Markov shifts, the algebraic type of continuous full groups, the Cuntz-Krieger algebras, and the K-theory dates of the Cuntz-Krieger algebras. This classification result shows that topological Markov shifts have deep connections with not only operator algebras but also groupoid theory, infinite non-amenable groups, group actions, graph theory, linear algebras, K-theory, and so on. By using this classification result, the complete classification of flow equivalence in two-sided topological Markov shifts is described in terms of Cuntz-Krieger algebras. The author will also study the relationship between the topological conjugacy of topological Markov shifts and the gauge actions of Cuntz-Krieger algebras.