C*-algebras PDF Download

Author: Robert S. Doran
Publisher: American Mathematical Soc.
ISBN: 9780821855041
Category : Mathematics
Languages : en
Pages : 436

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Book Description
The book contains carefully written expository and research articles by leaders in the field, including a reprint of the original 1943 paper on C[* algebras by Gelfand and Neumark.

Author: Robert S. Doran
Publisher: American Mathematical Soc.
ISBN: 0821851756
Category : Mathematics
Languages : en
Pages : 399

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Book Description
This volume contains the proceedings of an AMS Special Session held at the Joint Mathematics Meetings in San Antonio in January 1993 to celebrate the first fifty years of $C^*$-algebra theory. The book contains carefully written expository and research articles by leaders in the field. Also included is a reprinting of the original 1943 paper on $C^*$-algebras by Gelfand and Neumark, which has had such a profound influence on the field. The volume covers a broad spectrum of topics, including the Gelfand-Neumark theorems, $C^*$-algebras and quantization, projections in $C^*$-algebras, Mackey's theory of group representations and their relation to $C^*$-algebras, transformation group $C^*$-algebras, the influence of algebraic topology on $C^*$-algebras, K-theory and index theory in operator algebras, exponential rank in $C^*$-algebras, and a survey of the development of type III von Neumann algebras. With historical perspectives and up-to-date overviews to orient readers new to the field, this book will interest mathematicians, physicists, and mathematical historians.

Author: Robert S. Doran
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Author: Terry A. Loring
Publisher: American Mathematical Soc.
ISBN: 9780821871911
Category : Mathematics
Languages : en
Pages : 180

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Book Description
The techniques of universal algebra are applied to the category of C*-algebras. An important difference, central to this book, is that one can consider approximate representations of relations and approximately commuting diagrams. Moreover, the highly algebraic approach does not exclude applications to very geometric C*-algebras. K-theory is avoided, but universal properties and stability properties of specific C*-algebras that have applications to K-theory are considered. Index theory arises naturally, and very concretely, as an obstruction to stability for almost commuting matrices. Multiplier algebras are studied in detail, both in the setting of rings and of C*-algebras. Recent results about extensions of C*-algebras are discussed, including a result linking amalgamated products with the Busby/Hochshild theory.

Author: Ana Cannas da Silva
Publisher: American Mathematical Soc.
ISBN: 9780821809525
Category : Mathematics
Languages : en
Pages : 202

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Book Description
The volume is based on a course, ``Geometric Models for Noncommutative Algebras'' taught by Professor Weinstein at Berkeley. Noncommutative geometry is the study of noncommutative algebras as if they were algebras of functions on spaces, for example, the commutative algebras associated to affine algebraic varieties, differentiable manifolds, topological spaces, and measure spaces. In this work, the authors discuss several types of geometric objects (in the usual sense of sets with structure) that are closely related to noncommutative algebras. Central to the discussion are symplectic and Poisson manifolds, which arise when noncommutative algebras are obtained by deforming commutative algebras. The authors also give a detailed study of groupoids (whose role in noncommutative geometry has been stressed by Connes) as well as of Lie algebroids, the infinitesimal approximations to differentiable groupoids. Featured are many interesting examples, applications, and exercises. The book starts with basic definitions and builds to (still) open questions. It is suitable for use as a graduate text. An extensive bibliography and index are included.

Author: Toke M. Carlsen
Publisher: Springer
ISBN: 3319392867
Category : Mathematics
Languages : en
Pages : 348

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Book Description
Like the first Abel Symposium, held in 2004, the Abel Symposium 2015 focused on operator algebras. It is interesting to see the remarkable advances that have been made in operator algebras over these years, which strikingly illustrate the vitality of the field. A total of 26 talks were given at the symposium on a variety of themes, all highlighting the richness of the subject. The field of operator algebras was created in the 1930s and was motivated by problems of quantum mechanics. It has subsequently developed well beyond its initial intended realm of applications and expanded into such diverse areas of mathematics as representation theory, dynamical systems, differential geometry, number theory and quantum algebra. One branch, known as “noncommutative geometry”, has become a powerful tool for studying phenomena that are beyond the reach of classical analysis. This volume includes research papers that present new results, surveys that discuss the development of a specific line of research, and articles that offer a combination of survey and research. These contributions provide a multifaceted portrait of beautiful mathematics that both newcomers to the field of operator algebras and seasoned researchers alike will appreciate.

Author: Ernst Albrecht
Publisher: Springer Nature
ISBN: 3031505352
Category : Mathematics
Languages : en
Pages : 893

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Book Description
Over the course of his distinguished career, Jörg Eschmeier made a number of fundamental contributions to the development of operator theory and related topics. The chapters in this volume, compiled in his memory, are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Author: Liming Ge
Publisher: American Mathematical Soc.
ISBN: 0821810936
Category : Mathematics
Languages : en
Pages : 389

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Book Description
This volume contains the proceedings from the International Conference on Operator Algebras and Operator Theory held at the East China Normal University in Shanghai (China). Participants in the conference ranged from graduate students to postdocs to leading experts who came from around the world. Topics covered in this title were $C^*$-algebras, von Neumann algebras, non-self-adjoint operator algebras, wavelets, operator spaces and other related areas. This work consists of contributions from invited speakers and some mathematicians who were unable to attend. It presents important mathematical ideas while maintaining the uniqueness and excitement of this very successful event.

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: Huaxin Lin
Publisher: American Mathematical Soc.
ISBN: 147041466X
Category : Mathematics
Languages : en
Pages : 109

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Book Description
A unital separable -algebra, is said to be locally AH with no dimension growth if there is an integer satisfying the following: for any and any compact subset there is a unital -subalgebra, of with the form , where is a compact metric space with covering dimension no more than and is a projection, such that The authors prove that the class of unital separable simple -algebras which are locally AH with no dimension growth can be classified up to isomorphism by their Elliott invariant. As a consequence unital separable simple -algebras which are locally AH with no dimension growth are isomorphic to a unital simple AH-algebra with no dimension growth.