Derivations, Dissipations and Group Actions on C*-algebras PDF Download

Author: Ola Bratteli
Publisher: Springer
ISBN: 3540473769
Category : Mathematics
Languages : en
Pages : 283

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Author: Sergei Silvestrov
Publisher: Springer Nature
ISBN: 3031320093
Category : Mathematics
Languages : en
Pages : 833

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Book Description
The goal of the 2019 conference on Stochastic Processes and Algebraic Structures held in SPAS2019, Västerås, Sweden, from September 30th to October 2nd 2019 was to showcase the frontiers of research in several important topics of mathematics, mathematical statistics, and its applications. The conference has been organized along the following tracks: 1. Stochastic processes and modern statistical methods in theory and practice, 2. Engineering Mathematics, 3. Algebraic Structures and applications. This book highlights the latest advances in algebraic structures and applications focused on mathematical notions, methods, structures, concepts, problems, algorithms, and computational methods for the natural sciences, engineering, and modern technology. In particular, the book features mathematical methods and models from non-commutative and non-associative algebras and rings associated to generalizations of differential calculus, quantum deformations of algebras, Lie algebras, Lie superalgebras, color Lie algebras, Hom-algebras and their n-ary generalizations, semi-groups and group algebras, non-commutative and non-associative algebras and computational algebra interplay with q-special functions and q-analysis, topology, dynamical systems, representation theory, operator theory and functional analysis, applications of algebraic structures in coding theory, information analysis, geometry and probability theory. The book gathers selected, high-quality contributed chapters from several large research communities working on modern algebraic structures and their applications. The chapters cover both theory and applications, and are illustrated with a wealth of ideas, theorems, notions, proofs, examples, open problems, and results on the interplay of algebraic structures with other parts of Mathematics. The applications help readers grasp the material, and encourage them to develop new mathematical methods and concepts in their future research. Presenting new methods and results, reviews of cutting-edge research, open problems, and directions for future research, will serve as a source of inspiration for a broad range of researchers and students.

Author: H. Araki
Publisher: Springer Science & Business Media
ISBN: 1461204534
Category : Mathematics
Languages : en
Pages : 311

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Book Description
This volume consists of articles contributed by participants at the fourth Ja pan-U.S. Joint Seminar on Operator Algebras. The seminar took place at the University of Pennsylvania from May 23 through May 27, 1988 under the auspices of the Mathematics Department. It was sponsored and supported by the Japan Society for the Promotion of Science and the National Science Foundation (USA). This sponsorship and support is acknowledged with gratitude. The seminar was devoted to discussions and lectures on results and prob lems concerning mappings of operator algebras (C*-and von Neumann alge bras). Among the articles contained in these proceedings, there are papers dealing with actions of groups on C* algebras, completely bounded mappings, index and subfactor theory, and derivations of operator algebras. The seminar was held in honor of the sixtieth birthday of Sh6ichir6 Sakai, one of the great leaders of Functional Analysis for many decades. This vol ume is dedicated to Professor Sakai, on the occasion of that birthday, with the respect and admiration of all the contributors and the participants at the seminar. H. Araki Kyoto, Japan R. Kadison Philadelphia, Pennsylvania, USA Contents Preface.... ..... ....... ........... ...... ......... ................ ...... ............... ... vii On Convex Combinations of Unitary Operators in C*-Algebras UFFE HAAGERUP ......................................................................... .

Author: Edward Kissin
Publisher: CRC Press
ISBN: 9780582231573
Category : Mathematics
Languages : en
Pages : 620

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Book Description
This text provides a comprehensive treatment of representations on indefinite metric spaces, and their applications to the theory of *-derivations of C*-algebras. The book consists of two parts. The first studies the geometry of indefinite metric spaces (Krein and (Pi)(kappa)-spaces) and describes the theory of J-symmetric operator algebras and representations of *-algebras and groups on these spaces in a systematic form. For representations on (Pi)(kappa)-spaces, many significant new results are obtained; this establishes a possible approach to the general theory of representations. In the second part, different techniques of the theory of J-symmetric representations on Krein spaces are applied to the theory of *-derivations of C*-algebras implemented by skew-symmetric and dissipative operators. Various results are obtained, which establish a link between the deficiency indices of skew-symmetric operators implementing *-derivations of C*-algebras and dimensions of representations of these algebras. The problem of isomorphism of skew-symmetric operators is also touched upon. Numerous properties of the domains of *-derivations are investigated. These domains constitute an important subclass of differentiable Banach *-algebras, that is dense *-subalgebras of C*-algebras with properties in many respects similar to the properties of algebras of differentiable functions. The Weyl operator commutation relations are examined in the general context of *-derivations of C*-algebras. Powersí and Arvesonís indices of one-parameter semigroups of *-endomorphisms of the algebra B are considered, and various notions of the index of a *-derivation are introduced and studied. Application of the theory of J-symmetric representations on Krein spaces to the theory of *-derivations of C*-algebras is a new research area of growing interest and there are many exciting advances to be made in this field. The book covers a fairly large and complex body of material, and will serve as a stimulus to further research activity in this area.

Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 128

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Author: Palle E.T. Jorgensen
Publisher: Courier Dover Publications
ISBN: 0486822575
Category : Science
Languages : en
Pages : 304

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Book Description
Three-part treatment covers background material on definitions, terminology, operators in Hilbert space domains of representations, operators in the enveloping algebra, spectral theory; and covariant representation and connections. 2017 edition.

Author: Bruce Blackadar
Publisher: Taylor & Francis
ISBN: 9783540284864
Category : Mathematics
Languages : en
Pages : 552

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Book Description
This book offers a comprehensive introduction to the general theory of C*-algebras and von Neumann algebras. Beginning with the basics, the theory is developed through such topics as tensor products, nuclearity and exactness, crossed products, K-theory, and quasidiagonality. The presentation carefully and precisely explains the main features of each part of the theory of operator algebras; most important arguments are at least outlined and many are presented in full detail.

Author: Gianfausto Dell'Antonio
Publisher: Springer
ISBN: 9462391181
Category : Science
Languages : en
Pages : 459

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Book Description
The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics.

Author: Ola Bratteli
Publisher: Springer Science & Business Media
ISBN: 3662025205
Category : Technology & Engineering
Languages : en
Pages : 510

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Book Description
In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics. Subsequently we describe various applications to quantum statistical mechanics. At the outset of this project we intended to cover this material in one volume but in the course of develop ment it was realized that this would entail the omission ofvarious interesting topics or details. Consequently the book was split into two volumes, the first devoted to the general theory of operator algebras and the second to the applications. This splitting into theory and applications is conventional but somewhat arbitrary. In the last 15-20 years mathematical physicists have realized the importance of operator algebras and their states and automorphisms for problems of field theory and statistical mechanics. But the theory of 20 years aga was largely developed for the analysis of group representations and it was inadequate for many physical applications. Thus after a short honey moon period in which the new found tools of the extant theory were applied to the most amenable problems a longer and more interesting period ensued in which mathematical physicists were forced to redevelop the theory in relevant directions. New concepts were introduced, e. g. asymptotic abelian ness and KMS states, new techniques applied, e. g. the Choquet theory of barycentric decomposition for states, and new structural results obtained, e. g. the existence of a continuum of nonisomorphic type-three factors.

Author: Gianfausto Dell'Antonio
Publisher: Springer
ISBN: 9462391157
Category : Science
Languages : en
Pages : 381

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Book Description
The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics.