Partially ordered abelian groups with interpolation:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
1986
|
| Schriftenreihe: | Mathematical surveys and monographs
20 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001493097&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XXII, 336 S. |
| ISBN: | 0821815202 |
Internformat
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| 100 | 1 | |a Goodearl, Kenneth R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Partially ordered abelian groups with interpolation |c K. R. Goodearl |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1986 | |
| 300 | |a XXII, 336 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Mathematical surveys and monographs |v 20 | |
| 650 | 4 | |a Groupes abéliens | |
| 650 | 7 | |a Groupes abéliens |2 ram | |
| 650 | 4 | |a Interpolation | |
| 650 | 7 | |a Interpolation |2 ram | |
| 650 | 7 | |a Teoria Dos Grupos |2 larpcal | |
| 650 | 4 | |a Abelian groups | |
| 650 | 4 | |a Interpolation | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 411f 2001 B 1630 |
|---|---|
| DE-BY-TUM_katkey | 372027 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010612974 040020437610 |
| _version_ | 1821935626700718080 |
| adam_text | Contents
Preface ix
Prologue: Partially Ordered Grothendieck Groups xiii
NOTATIONAL CONVENTIONS xxi
1. Basic Notions l
• Partially ordered abelian groups • Infima and suprema
• Ideals and quotient groups • Categories of partially
ordered abelian groups • Pullbacks, pushouts, and
coproducts • Additional concepts
2. Interpolation 22
• Riesz interpolation and decomposition properties
• Ideals and quotient groups • Extensions • Products,
pullbacks, and pushouts • 2 unperforated interpolation
groups • Relatively bounded homomorphisms
3. Dimension Groups 44
• Dimension groups • Products, pullbacks, and pushouts
• Simplicial groups • Direct limits of simplicial groups
4. States 60
• Existence • Values of states • Uniqueness
• Additional uniqueness criteria • Discrete states
5. Compact Convex Sets 73
• Basic definitions • Categorical concepts • Extreme
points and faces • Separation by hyperplanes
• Existence of extreme points • Probability measures
• Faces of probability measures
V
vi CONTENTS
6. State Spaces 94
• Basic structure • Some examples • Functoriality
• Products and limits • Faces • Change of order unit
• Discrete states
7. Representation by Affine Continuous Functions 113
• Affine continuous function spaces • Affine
representations • Order unit norms • Bounded
homomorphisms
8. General Comparability 126
• Characteristic elements • Projection bases
• Comparability • Extremal states • Closures of faces
• Functional representations
9. DEDEKIND a COMPLETENESS 141
• Prototypical examples • Additional examples
• General comparability • Functional representations
10. CHOQUET SlMPLICES 153
• Simplices • Faces • Complementary faces
• Choquet simplices • Categorical properties
11. Affine Continuous Functions on Choquet Simplices 166
• Interpolation • Inverse limits • Semicontinuous
functions • Compact sets of extreme points • Closed
faces • Complementary faces
12. Metric Completions 188
• Completions with respect to positive homomorphisms
• Dedekind completeness • Completions with respect to
extremal states • Criterion for extremal states • Closed
faces
13. Affine Continuous Functions on State Spaces 207
• Approximations • Compact sets of extremal states
• Closed faces
14. Simple Dimension Groups 217
• Simplicity • State spaces • Classification
• Finite dimensional state spaces • Finite rank
15. Norm Completeness 236
• Norm completeness • Norm completions • Quotient
groups • Functional representations • Compact sets of
extremal states • Closed faces • Maximal ideals
CONTENTS vii
16. Countable Interpolation and Monotone
a C OMPLETENESS 263
• Countable interpolation • Monotone ^ completeness
• Norm completeness • Functional representations
• Compact sets of extremal states • Closed faces
• Quotient groups
17. Extensions of Dimension Groups 285
• Extensions • Some examples • Extensions with
order units • Some examples • Existence of extensions
with order units
Epilogue: Further K Theoretic Applications 309
Open Problems 317
Bibliography 325
Index 333
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| discipline | Mathematik |
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| id | DE-604.BV002272493 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T07:48:40Z |
| institution | BVB |
| isbn | 0821815202 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001493097 |
| oclc_num | 13395002 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-739 DE-355 DE-BY-UBR DE-12 DE-83 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-384 DE-739 DE-355 DE-BY-UBR DE-12 DE-83 DE-188 |
| physical | XXII, 336 S. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spellingShingle | Goodearl, Kenneth R. Partially ordered abelian groups with interpolation Mathematical surveys and monographs Groupes abéliens Groupes abéliens ram Interpolation Interpolation ram Teoria Dos Grupos larpcal Abelian groups Halbgeordnete abelsche Gruppe (DE-588)4571725-4 gnd Interpolation (DE-588)4162121-9 gnd Choquet-Simplex (DE-588)4209013-1 gnd Geordneter Vektorraum (DE-588)4156756-0 gnd |
| subject_GND | (DE-588)4571725-4 (DE-588)4162121-9 (DE-588)4209013-1 (DE-588)4156756-0 |
| title | Partially ordered abelian groups with interpolation |
| title_auth | Partially ordered abelian groups with interpolation |
| title_exact_search | Partially ordered abelian groups with interpolation |
| title_full | Partially ordered abelian groups with interpolation K. R. Goodearl |
| title_fullStr | Partially ordered abelian groups with interpolation K. R. Goodearl |
| title_full_unstemmed | Partially ordered abelian groups with interpolation K. R. Goodearl |
| title_short | Partially ordered abelian groups with interpolation |
| title_sort | partially ordered abelian groups with interpolation |
| topic | Groupes abéliens Groupes abéliens ram Interpolation Interpolation ram Teoria Dos Grupos larpcal Abelian groups Halbgeordnete abelsche Gruppe (DE-588)4571725-4 gnd Interpolation (DE-588)4162121-9 gnd Choquet-Simplex (DE-588)4209013-1 gnd Geordneter Vektorraum (DE-588)4156756-0 gnd |
| topic_facet | Groupes abéliens Interpolation Teoria Dos Grupos Abelian groups Halbgeordnete abelsche Gruppe Choquet-Simplex Geordneter Vektorraum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001493097&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT goodearlkennethr partiallyorderedabeliangroupswithinterpolation |
Inhaltsverzeichnis
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 411f 2001 B 1630 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |
| Exemplar 2 | Ausleihbar Am Standort |