An introduction to k-theory for c*-algebras:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2000
|
| Edition: | 1. publ. |
| Series: | London Mathematical Society: London Mathematical Society student texts
49 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XII, 242 S. |
| ISBN: | 0521783348 0521789443 9780521783347 9780521789448 |
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MARC
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| 100 | 1 | |a Rørdam, Mikael |d 1959- |e Verfasser |0 (DE-588)174092466 |4 aut | |
| 245 | 1 | 0 | |a An introduction to k-theory for c*-algebras |c M. Rørdam ; F. Larsen ; N. Laustsen |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2000 | |
| 300 | |a XII, 242 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society: London Mathematical Society student texts |v 49 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 7 | |a C* ÁLGEBRAS (ANÁLISE FUNCIONAL) |2 larpcal | |
| 650 | 7 | |a C*-algebra's |2 gtt | |
| 650 | 4 | |a C*-algèbres | |
| 650 | 7 | |a K-theorie |2 gtt | |
| 650 | 4 | |a K-théorie | |
| 650 | 4 | |a C*-algebras | |
| 650 | 4 | |a K-theory | |
| 650 | 0 | 7 | |a C-Stern-Algebra |0 (DE-588)4136693-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische K-Theorie |0 (DE-588)4141839-6 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a C-Stern-Algebra |0 (DE-588)4136693-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Larsen, Finn S. |e Verfasser |4 aut | |
| 700 | 1 | |a Laustsen, Niels Jakob |e Verfasser |4 aut | |
| 830 | 0 | |a London Mathematical Society: London Mathematical Society student texts |v 49 |w (DE-604)BV000841726 |9 49 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-009091645 | ||
Record in the Search Index
| _version_ | 1804128105926754304 |
|---|---|
| adam_text | Contents
Preface ix
1 C Algebra Theory 1
1.1 C* algebras and homomorphisms 1
1.2 Spectral theory 5
1.3 Matrix algebras 9
1.4 Exercises 10
2 Projections and Unitary Elements 15
2.1 Homotopy classes of unitary elements 15
2.2 Equivalence of projections 21
2.3 Semigroups of projections 28
2.4 Exercises 30
3 The Xo Group of a Unital C* Algebra 35
3.1 Definition of the A 0 group of a unital C* algebra 35
3.2 Functoriality of Ko 41
3.3 Examples 46
3.4 Exercises 54
4 The Functor Ko 59
4.1 Definition and functoriality of Ko 59
4.2 The standard picture of the group K0(A) 62
4.3 Half and split exactness and stability of ^o 66
4.4 Exercises 70
5 The Ordered Abelian Group K0{A) 77
5.1 The ordered A 0 group of stably finite C* algebras 77
5.2* States on K0(A) and traces on A 82
5.3 Exercises 83
v
vi CONTENTS
6 Inductive Limit C* Algebras 89
6.1 Products and sums of C* algebras 89
6.2 Inductive limits 91
6.3 Continuity of Ko 97
6.4* Stabilized C* algebras 101
6.5 Exercises 104
7 Classification of AF Algebras 109
7.1 Finite dimensional C* algebras 109
7.2 AF algebras 113
7.3 Elliott s classification theorem 118
7.4* UHF algebras 125
7.5 Exercises 130
8 The Functor Kx 133
8.1 Definition of the A^ group 133
8.2 Functoriality of Kx 138
8.3* A l groups and determinants 144
8.4 Exercises 147
9 The Index Map 153
9.1 Definition of the index map 154
9.2 The index map and partial isometries 158
9.3 An exact sequence of /{ groups 163
9.4* Fredholm operators and Fredholm index 165
9.5 Exercises 169
10 The Higher K Functors 175
10.1 The isomorphism between K (A) and Kq(SA) 175
10.2 The long exact sequence in /( theory 178
10.3 Exercises 182
11 Bott Periodicity 185
11.1 The Bott map 185
11.2 The proof of Bott periodicity 187
11.3 Applications of Bott periodicity 199
11.4* Homotopy groups and/( theory 201
11.5* The holomorphic function calculus 204
11.6 Exercises 206
CONTENTS vii
12 The Six Term Exact Sequence 209
12.1 The exponential map and the six term exact sequence 209
12.2 An explicit description of the exponential map 211
12.3 Exercises 215
13 Inductive Limits of Dimension Drop Algebras 219
13.1 Dimension drop algebras 219
13.2 Countable Abelian groups as /^ groups 222
13.3 Exercises 228
References 231
Table of K groups 234
Index of symbols 236
General index 239
|
| any_adam_object | 1 |
| author | Rørdam, Mikael 1959- Larsen, Finn S. Laustsen, Niels Jakob |
| author_GND | (DE-588)174092466 |
| author_facet | Rørdam, Mikael 1959- Larsen, Finn S. Laustsen, Niels Jakob |
| author_role | aut aut aut |
| author_sort | Rørdam, Mikael 1959- |
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| building | Verbundindex |
| bvnumber | BV013333102 |
| callnumber-first | Q - Science |
| callnumber-label | QA612 |
| callnumber-raw | QA612.33 |
| callnumber-search | QA612.33 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 230 SK 300 SK 600 |
| ctrlnum | (OCoLC)43661974 (DE-599)BVBBV013333102 |
| dewey-full | 512/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 |
| dewey-search | 512/.55 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV013333102 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:43:58Z |
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| isbn | 0521783348 0521789443 9780521783347 9780521789448 |
| language | English |
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| physical | XII, 242 S. |
| publishDate | 2000 |
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| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | London Mathematical Society: London Mathematical Society student texts |
| series2 | London Mathematical Society: London Mathematical Society student texts |
| spelling | Rørdam, Mikael 1959- Verfasser (DE-588)174092466 aut An introduction to k-theory for c*-algebras M. Rørdam ; F. Larsen ; N. Laustsen 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2000 XII, 242 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: London Mathematical Society student texts 49 Hier auch später erschienene, unveränderte Nachdrucke C* ÁLGEBRAS (ANÁLISE FUNCIONAL) larpcal C*-algebra's gtt C*-algèbres K-theorie gtt K-théorie C*-algebras K-theory C-Stern-Algebra (DE-588)4136693-1 gnd rswk-swf Algebraische K-Theorie (DE-588)4141839-6 gnd rswk-swf Algebraische K-Theorie (DE-588)4141839-6 s C-Stern-Algebra (DE-588)4136693-1 s DE-604 Larsen, Finn S. Verfasser aut Laustsen, Niels Jakob Verfasser aut London Mathematical Society: London Mathematical Society student texts 49 (DE-604)BV000841726 49 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009091645&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rørdam, Mikael 1959- Larsen, Finn S. Laustsen, Niels Jakob An introduction to k-theory for c*-algebras London Mathematical Society: London Mathematical Society student texts C* ÁLGEBRAS (ANÁLISE FUNCIONAL) larpcal C*-algebra's gtt C*-algèbres K-theorie gtt K-théorie C*-algebras K-theory C-Stern-Algebra (DE-588)4136693-1 gnd Algebraische K-Theorie (DE-588)4141839-6 gnd |
| subject_GND | (DE-588)4136693-1 (DE-588)4141839-6 |
| title | An introduction to k-theory for c*-algebras |
| title_auth | An introduction to k-theory for c*-algebras |
| title_exact_search | An introduction to k-theory for c*-algebras |
| title_full | An introduction to k-theory for c*-algebras M. Rørdam ; F. Larsen ; N. Laustsen |
| title_fullStr | An introduction to k-theory for c*-algebras M. Rørdam ; F. Larsen ; N. Laustsen |
| title_full_unstemmed | An introduction to k-theory for c*-algebras M. Rørdam ; F. Larsen ; N. Laustsen |
| title_short | An introduction to k-theory for c*-algebras |
| title_sort | an introduction to k theory for c algebras |
| topic | C* ÁLGEBRAS (ANÁLISE FUNCIONAL) larpcal C*-algebra's gtt C*-algèbres K-theorie gtt K-théorie C*-algebras K-theory C-Stern-Algebra (DE-588)4136693-1 gnd Algebraische K-Theorie (DE-588)4141839-6 gnd |
| topic_facet | C* ÁLGEBRAS (ANÁLISE FUNCIONAL) C*-algebra's C*-algèbres K-theorie K-théorie C*-algebras K-theory C-Stern-Algebra Algebraische K-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009091645&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000841726 |
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