An Introduction to the Classification of Amenable C*-Algebras,9789810246808

An Introduction to the Classification of Amenable C*-Algebras

by
ISBN13: 9789810246808
ISBN10: 9810246803
Format: Hardcover
Pub. Date: 2001-09-01
Publisher(s): WORLD SCIENTIFIC PUB CO INC
List Price: $125.00

Rent Textbook

Select for Price
Add to Cart
There was a problem. Please try again later.

Rent Digital

Rent Digital Options
Online:1825 Days access
Downloadable:Lifetime Access
$60.00
*To support the delivery of the digital material to you, a digital delivery fee of $3.99 will be charged on each digital item.
$60.00*
Add to Cart

New Textbook

We're Sorry
Sold Out

Used Textbook

We're Sorry
Sold Out

Summary

Introduces the recent development of the theory of the classification of amenable C*-algebras-- the first such attempt. The first three chapters present the basics of the theory of C*-algebras which are particularly important to the theory of the classification of amenable C*-algebras.

Table of Contents

Preface vii
The Basics of C*-algebras
1(66)
Banach algebras
1(8)
C*-algebras
9(3)
Commutative C*-algebras
12(4)
Positive cones
16(4)
Approximate identities, hereditary C*-subalgebras and quotients
20(5)
Positive linear functionals and a Gelfand-Naimark theorem
25(7)
Von Neumann algebras
32(6)
Enveloping von Neumann algebras and the spectral theorem
38(4)
Examples of C*-algebras
42(9)
Inductive limits of C*-algebras
51(9)
Exercises
60(5)
Addenda
65(2)
Amenable C*-algebras and K-theory
67(46)
Completely positive linear maps and the Stinespring representation
67(5)
Examples of completely positive linear maps
72(4)
Amenable C*-algebras
76(6)
K-theory
82(7)
Perturbations
89(8)
Examples of K-groups
97(6)
K-theory of inductive limits of C*-algebras
103(5)
Exercises
108(3)
Addenda
111(2)
AF-algebras and Ranks of C*-algebras
113(52)
C*-algebras of stable rank one and their K-theory
113(7)
C*-algebras of lower rank
120(7)
Order structure of K-theory
127(6)
AF-algebras
133(7)
Simple C*-algebras
140(6)
Tracial topological rank
146(8)
Simple C*-algebras with TR(A) ≤ 1
154(6)
Exercises
160(2)
Addenda
162(3)
Classification of Simple AT-algebras
165(46)
Some basics about AT-algebras
165(5)
Unitary groups of C*-algebras with real rank zero
170(7)
Simple AT-algebras with real rank zero
177(5)
Unitaries in simple C*-algebra with RR(A) = 0
182(4)
A uniqueness theorem
186(6)
Classification of simple AT-algebras
192(4)
Invariants of simple AT-algebras
196(8)
Exercises
204(4)
Addenda
208(3)
C*-algebra Extensions
211(58)
Multiplier algebras
211(6)
Extensions of C*-algebras
217(4)
Completely positive maps to Mn(C)
221(6)
Amenable completely positive maps
227(6)
Absorbing extensions
233(10)
A stable uniqueness theorem
243(7)
K-theory and the universal coefficient theorem
250(5)
Characterization of KK-theory and a universal multi-coefficient theorem
255(4)
Approximately trivial extensions
259(6)
Exercises
265(4)
Classification of Simple Amenable C*-algebras
269(38)
An existence theorem
269(10)
Simple AH-algebras
279(9)
The classification theorems
288(7)
Invariants and some isomorphism theorems
295(12)
Bibliography 307(10)
Index 317

An electronic version of this book is available through VitalSource.

This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.

By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.

Digital License

You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.

More details can be found here.

A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.

Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.

Please view the compatibility matrix prior to purchase.