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An Invitation to C*-Algebras

Author: William Arveson
Publisher: New York, NY : Springer New York, 1976.
Series: Graduate texts in mathematics, 39.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book is an introduction to C^*-algebras and their representations on Hilbert spaces. The presentation is as simple and concrete as possible; the book is written for a second-year graduate student who is familiar with the basic results of functional analysis, measure theory and Hilbert spaces. The author does not aim for great generality, but confines himself to the best-known and also to the most important  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: William Arveson
ISBN: 9781461263715 1461263719
OCLC Number: 852789612
Description: 1 online resource (x, 106 pages).
Contents: 1 Fundamentals --
1.1. Operators and C*-algebras --
1.2. Two density theorems --
1.3. Ideals, quotients, and representations --
1.4. C*-algebras of compact operators --
1.5. CCR and GCR algebras --
1.6. States and the GNS construction --
1.7. The existence of representations --
1.8. Order and approximate units --
2 Multiplicity Theory --
2.1. From type I to multiplicity-free --
2.2. Commutative C*-algebras and normal operators --
2.3. An application: type I von Neumann algebras --
2.4. GCR algebras are type I --
3 Borel Structures --
3.1. Polish spaces --
3.2. Borel sets and analytic sets --
3.3. Borel spaces --
3.4. Cross sections --
4 From Commutative Algebras to GCR Algebras --
4.1. The spectrum of a C*-algebra --
4.2. Decomposable operator algebras --
4.3. Representations of GCR algebras.
Series Title: Graduate texts in mathematics, 39.
Responsibility: by William Arveson.

Abstract:

This book gives an introduction to C*-algebras and their representations on Hilbert spaces. But insofar as representations are con- cerned, we can point to the empirical fact that to this day no one  Read more...

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