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An introduction to C*-algebras and t...

Perera, Francesc.

An introduction to C*-algebras and the classification program

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	An introduction to C*-algebras and the classification programby Karen R. Strung ; edited by Francesc Perera.
作者:	Strung, Karen R.
其他作者:	Perera, Francesc.
出版者:	Cham :Springer International Publishing :2021.
面頁冊數:	xiii, 322 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	C*-algebras.
電子資源:	https://doi.org/10.1007/978-3-030-47465-2
ISBN:	9783030474652$q(electronic bk.)

An introduction to C*-algebras and the classification program
Strung, Karen R.

An introduction to C*-algebras and the classification program[electronic resource] /by Karen R. Strung ; edited by Francesc Perera. - Cham :Springer International Publishing :2021. - xiii, 322 p. :ill., digital ;24 cm. - Advanced courses in mathematics - CRM Barcelona,2297-0304. - Advanced courses in mathematics - CRM Barcelona..

Banach algebras and spectral theory -- The Gelfand representation -- C*-algebra basics -- Positive elements -- Positive linear functionals and representations -- Weak and strong operator topologies and von Neumann algebras -- Tensor products for C*-algebras -- Completely positive maps -- Inductive limits and approximately finite (AF) C*-algebras -- Group C*-algebras and crossed products -- Cuntz algebras -- Quasidiagonal C*-algebras -- K-theory for unital C*-algebras -- Classification of AF-algebras -- Nuclear dimension -- Strongly self-absorbing algebras -- The Jiang-Su algebra -- Strict comparison and the Cuntz semigroup -- The Classification Theorem and the Toms-Winter Theorem.

This book is directed towards graduate students that wish to start from the basic theory of C*-algebras and advance to an overview of some of the most spectacular results concerning the structure of nuclear C*-algebras. The text is divided into three parts. First, elementary notions, classical theorems and constructions are developed. Then, essential examples in the theory, such as crossed products and the class of quasidiagonal C*-algebras, are examined, and finally, the Elliott invariant, the Cuntz semigroup, and the Jiang-Su algebra are defined. It is shown how these objects have played a fundamental role in understanding the fine structure of nuclear C*-algebras. To help understanding the theory, plenty of examples, treated in detail, are included. This volume will also be valuable to researchers in the area as a reference guide. It contains an extensive reference list to guide readers that wish to travel further.

ISBN: 9783030474652$q(electronic bk.)

Standard No.: 10.1007/978-3-030-47465-2doiSubjects--Topical Terms:

306364
C*-algebras.

LC Class. No.: QA326

Dewey Class. No.: 512.55

An introduction to C*-algebras and the classification program
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245 1 3 $a An introduction to C*-algebras and the classification program $h [electronic resource] / $c by Karen R. Strung ; edited by Francesc Perera.
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505 0 $a Banach algebras and spectral theory -- The Gelfand representation -- C*-algebra basics -- Positive elements -- Positive linear functionals and representations -- Weak and strong operator topologies and von Neumann algebras -- Tensor products for C*-algebras -- Completely positive maps -- Inductive limits and approximately finite (AF) C*-algebras -- Group C*-algebras and crossed products -- Cuntz algebras -- Quasidiagonal C*-algebras -- K-theory for unital C*-algebras -- Classification of AF-algebras -- Nuclear dimension -- Strongly self-absorbing algebras -- The Jiang-Su algebra -- Strict comparison and the Cuntz semigroup -- The Classification Theorem and the Toms-Winter Theorem.
520 $a This book is directed towards graduate students that wish to start from the basic theory of C*-algebras and advance to an overview of some of the most spectacular results concerning the structure of nuclear C*-algebras. The text is divided into three parts. First, elementary notions, classical theorems and constructions are developed. Then, essential examples in the theory, such as crossed products and the class of quasidiagonal C*-algebras, are examined, and finally, the Elliott invariant, the Cuntz semigroup, and the Jiang-Su algebra are defined. It is shown how these objects have played a fundamental role in understanding the fine structure of nuclear C*-algebras. To help understanding the theory, plenty of examples, treated in detail, are included. This volume will also be valuable to researchers in the area as a reference guide. It contains an extensive reference list to guide readers that wish to travel further.
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