An Invitation to C*-Algebras (Graduate Texts in Mathematics 39)
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An Invitation to C*-Algebras (Graduate Texts in Mathematics 39)
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Artikelmerkmale
- Artikelzustand
- Release Year
- 1976
- Book Title
- An Invitation to C*-Algebras (Graduate Texts in Mathematics 39)
- ISBN
- 9780387901763
Über dieses Produkt
Product Identifiers
Publisher
Springer New York
ISBN-10
0387901760
ISBN-13
9780387901763
eBay Product ID (ePID)
144259
Product Key Features
Number of Pages
X, 108 Pages
Language
English
Publication Name
Invitation to C-Algebras
Publication Year
1976
Subject
Functional Analysis, Algebra / General
Type
Textbook
Subject Area
Mathematics
Series
Graduate Texts in Mathematics Ser.
Format
Hardcover
Dimensions
Item Weight
35.6 Oz
Item Length
10 in
Item Width
7 in
Additional Product Features
Edition Number
2
Intended Audience
Scholarly & Professional
LCCN
76-003656
TitleLeading
An
Dewey Edition
21
Series Volume Number
39
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
512/.55
Table Of Content
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.
Synopsis
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 parts of the theory and the applications., This book gives an introduction to C*-algebras and their representations on Hilbert spaces. We have tried to present only what we believe are the most basic ideas, as simply and concretely as we could. So whenever it is convenient (and it usually is), Hilbert spaces become separable and C*-algebras become GCR. This practice probably creates an impression that nothing of value is known about other C*-algebras. Of course that is not true. But insofar as representations are con cerned, we can point to the empirical fact that to this day no one has given a concrete parametric description of even the irreducible representations of any C*-algebra which is not GCR. Indeed, there is metamathematical evidence which strongly suggests that no one ever will (see the discussion at the end of Section 3. 4). Occasionally, when the idea behind the proof of a general theorem is exposed very clearly in a special case, we prove only the special case and relegate generalizations to the exercises. In effect, we have systematically eschewed the Bourbaki tradition. We have also tried to take into account the interests of a variety of readers. For example, the multiplicity theory for normal operators is contained in Sections 2. 1 and 2. 2. (it would be desirable but not necessary to include Section 1. 1 as well), whereas someone interested in Borel structures could read Chapter 3 separately. Chapter I could be used as a bare-bones introduction to C*-algebras. Sections 2., This book gives an introduction to C*-algebras and their representations on Hilbert spaces. We have tried to present only what we believe are the most basic ideas, as simply and concretely as we could. So whenever it is convenient (and it usually is), Hilbert spaces become separable and C*-algebras become GCR. This practice probably creates an impression that nothing of value is known about other C*-algebras. Of course that is not true. But insofar as representations are con- cerned, we can point to the empirical fact that to this day no one has given a concrete parametric description of even the irreducible representations of any C*-algebra which is not GCR. Indeed, there is metamathematical evidence which strongly suggests that no one ever will (see the discussion at the end of Section 3. 4). Occasionally, when the idea behind the proof of a general theorem is exposed very clearly in a special case, we prove only the special case and relegate generalizations to the exercises. In effect, we have systematically eschewed the Bourbaki tradition. We have also tried to take into account the interests of a variety of readers. For example, the multiplicity theory for normal operators is contained in Sections 2. 1 and 2. 2. (it would be desirable but not necessary to include Section 1. 1 as well), whereas someone interested in Borel structures could read Chapter 3 separately. Chapter I could be used as a bare-bones introduction to C*-algebras. Sections 2., 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 parts of the theory and the applications.
LC Classification Number
QA150-272
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98,6% positive Bewertungen•103 Tsd. Artikel verkauft
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Verkäuferbewertungen (31'298)
- l***o (115)- Bewertung vom Käufer.Letzte 6 MonateBestätigter KaufPackage arrived from Skokie, IL to southeast Michigan in three days. Book was wrapped well in an large outer plastic mailing envelope and in a second large plastic mailing envelope inside . Book was in the condition described and even has the errata sheet insert. I had no problems with the seller, and I would buy from them again. Good sale.
- v***n (68)- Bewertung vom Käufer.Letzter MonatBestätigter KaufThe seller supplied additional photos showing that the books included both dust jackets as described. The books arrived well on time and were in a like new condition. They were also well packaged. This was of great value. Thank you very much. Perfect.
- p***e (1215)- Bewertung vom Käufer.Letzte 6 MonateBestätigter KaufPurchased on 08.26.2025 and rec'd as described on 09.02.2025 (after Labor Day holiday). Two text books were individually wrapped in plastic, wrapped together in another plastic baggie and then placed in a padded envelope. Very happy w/ the extra protection taken in shipping the text books. Thank you.