K-theory and C*-algebras: a friendly approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2004
|
| Ausgabe: | reprint. |
| Schriftenreihe: | Oxford science publications
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 370 S. graph. Darst. |
| ISBN: | 0198596944 |
Internformat
MARC
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| 100 | 1 | |a Wegge-Olsen, Niels E. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a K-theory and C*-algebras |b a friendly approach |c N. E. Wegge-Olsen |
| 250 | |a reprint. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2004 | |
| 300 | |a XII, 370 S. |b graph. Darst. | ||
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| 337 | |b n |2 rdamedia | ||
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Datensatz im Suchindex
| _version_ | 1804139205075402752 |
|---|---|
| adam_text | Contents
General
notation
χι
0
Introduction
1
0.1
How to read this book
1
0.2
What is K-theory?
2
0.3
Brutal synopsis of the book
8
Part I C*-algebras
C*-algebras
—
a summary
15
1.1
C*-algebras
15
1.2
Units and approximate units
16
1.3
Spectral theory
17
1.4
Ideals
18
1.5
Operator algebras and representations
18
1.6
Positivity
20
1.7
Infinite sums
20
1.8
Inductive limits
21
1.9
Tensor products
21
1.10
Stabilization
22
1.11
Non-commutative topology
24
1.12
Exercises
25
Multiplier algebras
26
2.1
Unitizations
27
2.2
Multipliers and double centralizers
31
2.3
Strict topology
39
2.4
Exercises
44
Extensions of C*-algebras
51
3.1
Exact sequences
52
3.2
Extensions and the Busby invariant
55
3.3
Sums of extensions
61
3.4
Exercises
65
Vlil
Contents
Invertibles and unitaries
4.1
Normalized matrices
4.2
Homotopies
4.3
Lifting results
4.4
Inductive limits
4.5
Exercises
73
73
75
80
82
5
Projections
85
5.1
Partial isometries and projections
85
5.2
Equivalence of projections
88
5.3
Decomposition into matrix algebras
93
5.4
Exercises
100
Part II Fundamentals of K-theory
6
Kq
—
basic properties
107
6.1
The monoid V(A)
109
6.2
The group K0(A)
110
6.3
Exact sequences
119
6.4
Homotopy
invariance
121
6.5
Catalogue of basic K-groups
123
6.6
Exercises
124
7
iřj
and suspensions
130
7.1
TheK-groupJCit-A)
130
7.2
Suspended C*-algebras
136
7.3
Exercises
144
8
The index map in K-theory
146
8.1
Definition of the connecting map
146
8.2
The long exact sequence
149
8.3
Exercises
154
9
Bott
periodicity
158
9.1
The
Bott
map
159
9.2
Approximation by loops
161
9.3
The cyclic six term exact sequence
169
9.4
Exercises
172
10
K-theory for multiplier algebras
180
Contents ix
11
Homology
184
11.1 Homology
functors
184
11.2
Bott
periodicity and functorial K-theory
190
11.3
Exercises
195
12
Some examples: AF-algebras, Cuntz algebras,
rotation algebras
196
12.1
AF-algebras
196
12.2
The Cuntz algebras On
201
12.3
The (irrational) rotation algebras Ae
202
12.4
Exercises
206
13
Vector bundles and topological K-theory
210
13.1
Vector bundles and the semigroup V(X)
211
13.2
Functoriality
213
13.3
TheK-groups
214
13.4
Sections
217
13.5
Exercises
219
Part III Hilbert modules and a
GENERALIZED INDEX THEORY
14
The classical
Fredholm
index
225
14.1
The index and its properties
225
14.2
Exercises
229
15
Hilbert modules
231
15.1
Hilbert modules
232
15.2
Adjointable operators
240
15.3
Complementability and polar decompositions
248
15.4
Finitely and countably generated
projective
modules
254
15.5
Exercises
259
16
The Kuiper-Mingo theorem
269
17
A generalized
Fredholm
index
277
17.1
The generalized Atkinson theorem
278
17.2
Definition of the generalized
Fredholm
index
281
17.3
Properties of the index map
285
x
Contents
Part IV Appendices
G
The Grothendieck group
295
L
Inductive limits
298
L.I Algebraic direct limits
298
L.2 C*-algebraic inductive limits
302
O (Dis)order
and
positivity
in C*-algebras
305
T
Tensor products
—
or: the importance of being
subcross
309
T.I Introduction
309
T.2 Algebraic tensor products
313
T.3 Norms on algebraic tensor products
323
T.4 Tensor product of Hubert spaces
328
T.5 The spatial tensor product
331
T.6 Other C*-algebra tensor products
343
T.7 Exercises
356
References
362
Subject index
367
|
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| author_sort | Wegge-Olsen, Niels E. |
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| bvnumber | BV035557512 |
| classification_rvk | SK 230 SK 300 |
| classification_tum | MAT 552f MAT 467f |
| ctrlnum | (OCoLC)612594280 (DE-599)BVBBV035557512 |
| discipline | Mathematik |
| edition | reprint. |
| format | Book |
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| indexdate | 2024-07-09T21:40:23Z |
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| isbn | 0198596944 |
| language | English |
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| spelling | Wegge-Olsen, Niels E. Verfasser aut K-theory and C*-algebras a friendly approach N. E. Wegge-Olsen reprint. Oxford [u.a.] Oxford Univ. Press 2004 XII, 370 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford science publications C-Stern-Algebra (DE-588)4136693-1 gnd rswk-swf K-Theorie (DE-588)4033335-8 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content K-Theorie (DE-588)4033335-8 s DE-604 C-Stern-Algebra (DE-588)4136693-1 s Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017613310&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Wegge-Olsen, Niels E. K-theory and C*-algebras a friendly approach C-Stern-Algebra (DE-588)4136693-1 gnd K-Theorie (DE-588)4033335-8 gnd |
| subject_GND | (DE-588)4136693-1 (DE-588)4033335-8 (DE-588)4123623-3 |
| title | K-theory and C*-algebras a friendly approach |
| title_auth | K-theory and C*-algebras a friendly approach |
| title_exact_search | K-theory and C*-algebras a friendly approach |
| title_full | K-theory and C*-algebras a friendly approach N. E. Wegge-Olsen |
| title_fullStr | K-theory and C*-algebras a friendly approach N. E. Wegge-Olsen |
| title_full_unstemmed | K-theory and C*-algebras a friendly approach N. E. Wegge-Olsen |
| title_short | K-theory and C*-algebras |
| title_sort | k theory and c algebras a friendly approach |
| title_sub | a friendly approach |
| topic | C-Stern-Algebra (DE-588)4136693-1 gnd K-Theorie (DE-588)4033335-8 gnd |
| topic_facet | C-Stern-Algebra K-Theorie Lehrbuch |
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