Finite von Neumann algebras and masas:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | London Mathematical Society lecture note series
351 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 400 S. |
| ISBN: | 9780521719193 |
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| 245 | 1 | 0 | |a Finite von Neumann algebras and masas |c Allan M. Sinclair ; Roger R. Smith |
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Datensatz im Suchindex
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| adam_text | FINITE VON NEUMANN ALGEBRAS AND MASAS ALLAN M. SINCLAIR UNIVERSITY OF
EDINBURGH ROGER R. SMITH ! TEXAS A&M UNIVERSITY CONTENTS PREFACE *
IX 1 GENERAL INTRODUCTION * * *. J * ! ; , J 1.1- SYNOPSIS * .
.*. .*. . : J K ..*.*.. ; ; . *. : . :*; *.!. . *. 1 1.2 F U R T H E R R
E S U L T S . . . . . . . . . . . . . - . . . . . . . ... . : : .
.-. . * 3 2 * M A S A S I N B ( H ) . * ; * * * . . * * * . ,. ..
*. -. ,.*..*;* 5 .2.1 INTRODUCTION ; ;) . . . . . . . . 5 .2.2
STANDARD THEOREMS *.-.; . *!. . . .1. **.*....... 5 2.3 MASAS :
;,..,:..*...;. 8 2.4 MASAS IN TYPE L N ALGEBRAS 13 3 FINITE YON NEUMANN
ALGEBRAS , , , , R ; 17 3.1 INTRODUCTION ... .,. ;: 17 . 3.2 FINITE
ALGEBRAS :..., ..., .,.,...,. ...,,.., . .-*;. ..-.* 18 !. 3.3 EXAMPLES
OF MASAS FROM GROUPS . , R . . . . . . . . . . . . . . . . . . 21 3.4
TENSOR PRODUCTS AND CROSSED PRODUCTS 7 . ........ . . . ........ ; . .
*. 27 3.5 DIFFUSE ABELIAN ALGEBRAS . . . . ... . . .. .,. . . . ........
. .-. . ; . S 34 3.6 CONDITIONAL EXPECTATIONS . . . ... . . .1 . /..,,.
. . . 37 3.7 GROUP VON NEUMANN ALGEBRAS REVISITED . 48 .3.8
HYPERFINITENESS .. J ... . 49 4 THE BASIC CONSTRUCTION 5 2 41
INTRODUCTION . . . . . . . . . . ; . . . . 52 4.2 PROPERTIES . . . :
V .-. . : . ... .! 53 4.3- THE TRACE ON {N, E B ) . : . V . : ? .
R . : : ... .: S : 56 4.4 EXAMPLES . . . 73 4.5 THE PULL-DOWN MAP
.... . !;. . 76 5 PROJECTIONS AND PARTIAL ISOMETRIES * ***** - * *
. 80 5 1 INTRODUCTION . . [ .* . . . . . . : *. . ! . 80 5.2 C O M P
A R I S O N OF T W O PROJECTIONS! : . ., J .: . .-. . .. .*. ... . . . .
. 80 5.3. A P P R O X I M A T I O N S OF PROJECTIONS .,..:;.*. ..
..*. .* ... . :. . ; . . .. ;.* 88 ; 5.4 C O M M U T A N T S OF
COMPRESSIONS . . .. . . . ...**.- . . : .., : . . :*.*...*. . . 91 VI
CONTENTS 5.5 BASIC LEMMAS FOR KADISON S RESULTS 93 5.6 RANGE OF THE
CENTRE-VALUED TRACE 95 6 NORMALISERS, ORTHOGONALITY AND DISTANCES 98 6.1
INTRODUCTION 98 6.2 NORMALISERS OF MASAS ,98 6.3 ORTHOGONALITY OF VON
NEUMANN SUBALGEBRAS ;.-.... : ......*.*. 104 6.4 DISTANCES BETWEEN
SUBALGEBRAS 106 7 THE PUKANSZKY INVARIANT 113 7.1 INTRODUCTION . . 113 .
7.2 THE ALGEBRAS A, A, A AND J F(A) INTERACT 116 7.3 PROPERTIES OF THE
PUKANSZKY INVARIANT . . . 120 7.4 THE PUKANSZKY INVARIANT IN GROUP
FACTORS .. ..,. ...,*..,: * * .... 123 7.5 EXAMPLES OF THE PUKANSZKY
INVARIANT 130 7.6 OPEN PROBLEMS 136 8 OPERATORS IN L[0,L]B(I/) . .
137 8.1 INTRODUCTION .**;* ..*:. . . . :. . . 137 8.2 MATRIX
COMPUTATIONS ; . ... .*.. . . . 137 8.3 MAIN RESULTS . . . . . . . . K .
. . . 141 9 PERTURBATIONS 148 * 9.1 INTRODUCTION V-.-Y. . . :. .. . . :
: . . . . 148 ; 9.2 AVERAGING ES OVER A . . . . . . . . . 150 9.3
PERTURBING SUBALGEBRAS IN THE UNIFORM NORM . . * * *.* * * * * * * 156
9.4 LEMMAS ON CLOSE SUBALGEBRAS : . . *: . . . . . . . . . . . .
. . . . 159 9.5 DISTANCES AND GROUPOID HORMAIISERS . . . . . . . ., .
. . . . . . . . .174 9.6 NUMERICAL CONSTANTS FOR PERTURBATIONS . . . .
. . . . . . . . . . . . 176 9.7 PERTURBATIONS OF MASAS BY AVERAGING .
. . . . . . . . .. . . .,. . . 183 10 GENERAL PERTURBATIONS !
186 . 10.1 INTRODUCTION . ( . . , ... . ... ......... 186 10.2 THE JONES
INDEX . . . . . .. ..... , ,,*. . . 186 10.3 CONTAINMENT OF FINITE
ALGEBRAS ,. 189 10.4 CLOSE VON NEUMANN ALGEBRAS . H . .... . .,. . .,
193 11 SINGULAR MASAS . . ,-. 198 11.1 INTRODUCTION . . * . . . . . . .
: . . . . / 198 :* 11.2 BASIC LEMMAS . !; . .;.,.;, . : .-. .-. .
.-.-*;. .,;.....:-;.. 200 11.3 SINGULAR TO WAHP .,.,. : . I, . ..I.
...,.203 11.4 A BASIS CONDITION FOR SINGULARITY .... . . . . ; . . . . ;
.-. : . . . 208 11.5 ENUMERATION OF WORDS IN F2 . . . . . . .
...*.:..*.*..-...*. J. 212 : 11.6 THE LAPLACIAN MASA *.-. : .- *:.- .
....:..*. : . . . 218 CONTENTS VII 12 EXISTENCE OF SPECIAL MASAS 223
12.1 INTRODUCTION . . , 223 12.2 APPROXIMATIONS IN SUBALGEBRAS 224 12.3
CONSTRUCTING SEMIREGULAR MASAS 229 12.4 CONSTRUCTING SINGULAR MASAS 232
12.5 SINGULARITY AND AUTOMORPHISMS 239 13 IRREDUCIBLE HYPERFINITE
SUBFACTORS 242 13.1 INTRODUCTION 242 13.2 IRREDUCIBLE HYPERFINITE
SUBFACTORS EXIST 242 13.3 CARTAN MASAS IN HYPERFINITE SUBFACTORS 246
13.4 PROPERTY F 248 13.5 IRREDUCIBLE HYPERFINITES IN F FACTORS 253 14
MAXIMAL INJECTIVE SUBALGEBRAS 257 14.1 INTRODUCTION 257 14.2 MAXIMAL
INJECTIVITY AND MASAS 258 14.3 MAXIMAL INJECTIVITY OF SUBFACTORS 263 15
MASAS IN NON-SEPARABLE FACTORS 268 15.1 INTRODUCTION 268 15.2 MASAS IN
TV 268 15.3 MASAS IN L(F S ) 275 16 SINGLY GENERATED HI FACTORS 278
16.1 INTRODUCTION 278 16.2 NOTATION AND DEFINITIONS 279 16.3 EXAMPLES
AND BASIC LEMMAS 283 16.4 THE SCALING FORMULA FOR Q 289 16.5
INTERPOLATED FREE GROUP FACTORS AND Q 296 16.6 SINGLE GENERATION 298
16.7 MAIN TECHNICAL LEMMAS 302 16.8 EXAMPLES OF SINGLY GENERATED HI
FACTORS 311 A THE ULTRAPOWER AND PROPERTY F 316 A.I INTRODUCTION 316 A.2
ULTRAFILTERS AND CHARACTERS 317 A.3 MAXIMAL QUOTIENTS OF FINITE ALGEBRAS
319 A.4 THE ALGEBRA N% 325 A.5 THE ULTRAPOWER N U 328 A.6 RELATIVE
COMMUTANTS IN TV 334 A.7 PROPERTY F. REVISITED 337 VIII CONTENTS B
UNBOUNDED OPERATORS 342 B.I INTRODUCTION 342 B.2 BASIC RESULTS . 342 B.3
THE FUNCTIONAL CALCULUS 348 B.4 OPERATORS FROM L 2 (N) 359 B.5
OPERATORS FROM L^N) 362 C THE TRACE REVISITED 373 C.I INTRODUCTION 373
C.2 PRELIMINARY LEMMAS 373 C.3 CONSTRUCTION OF THE TRACE 375
BIBLIOGRAPHY 379 INDEX 394 INDEX OF SYMBOLS 398
|
| adam_txt |
FINITE VON NEUMANN ALGEBRAS AND MASAS ALLAN M. SINCLAIR UNIVERSITY OF
EDINBURGH ROGER R. SMITH ! TEXAS A&M UNIVERSITY CONTENTS PREFACE ' ' ' *
IX 1 GENERAL INTRODUCTION * * *. J * ! ; , J 1.1- SYNOPSIS '*''.
.*.'.*.'. : J K .*.*. ; ; . *. : . :*;'*.!. .'*. 1 1.2 F U R T H E R R
E S U L T S . . . . . . . . . . . . . - . . . . . ' . . . . : : '.
.-.'.'* 3 2 * M A S A S I N B ( H ) . * ; * * * . . * * ' * . ,.\ .
*. -. ,.*.*;* 5 .2.1 INTRODUCTION ; ;) . . . . . . . . 5 .2.2
STANDARD THEOREMS *.-.; . *!. . . .1. **.*. 5 2.3 MASAS :
;,.,:.*.;. 8 2.4 MASAS IN TYPE L N ALGEBRAS 13 3 FINITE YON NEUMANN
ALGEBRAS , , , , R ; 17 3.1 INTRODUCTION . .,. ;: 17 . 3.2 FINITE
ALGEBRAS :., ., .,.,.,. .,,., . .-*;. .-.* 18 !. 3.3 EXAMPLES
OF MASAS FROM GROUPS . , R . . . . . . . . . . . . . . . . . . 21 3.4
TENSOR PRODUCTS AND CROSSED PRODUCTS 7 . . . . . . ; . .
*. 27 3.5 DIFFUSE ABELIAN ALGEBRAS . . . . . . . .'.,. . . . .
. .-. . ; . S 34 3.6 CONDITIONAL EXPECTATIONS . . . . . . .1 . /.,,.
. .'. 37 3.7 GROUP VON NEUMANN ALGEBRAS REVISITED . 48 .3.8
HYPERFINITENESS . J . . 49 4 THE BASIC CONSTRUCTION ' 5 2 41
INTRODUCTION . . . . . . . . . . ; . . . .' 52 4.2 PROPERTIES .''.'.':
V'.-.'". : . .'.!' 53 '4.3- THE TRACE ON {N, E B ) . \ :'. V'. : ?'. '
R . :' : .'.: S : 56 4.4 EXAMPLES . . . 73 4.5 THE PULL-DOWN MAP
'.'. !;."".' 76 5 PROJECTIONS AND PARTIAL ISOMETRIES * *****''- *'* '
. 80 5 1 INTRODUCTION'. .'[".*''. . . . . .': '*. . ! .' 80 5.2 C O M P
A R I S O N OF T W O PROJECTIONS! :'.'., J .: . .-. . .'.*.". . . . .
. 80 5.3. A P P R O X I M A T I O N S OF PROJECTIONS .,.:;.*. .
.*.".* . . :. . ; . . . ;.* 88 ; 5.4 C O M M U T A N T S OF
COMPRESSIONS . . .'. . .'.**.- . . : ., : . . :*.*.*. . . 91 VI
CONTENTS 5.5 BASIC LEMMAS FOR KADISON'S RESULTS 93 5.6 RANGE OF THE
CENTRE-VALUED TRACE 95 6 NORMALISERS, ORTHOGONALITY AND DISTANCES 98 6.1
INTRODUCTION 98 6.2 NORMALISERS OF MASAS ,98 6.3 ORTHOGONALITY OF VON
NEUMANN SUBALGEBRAS ;.-. : .*.*. 104 6.4 DISTANCES BETWEEN
SUBALGEBRAS 106 7 THE PUKANSZKY INVARIANT 113 7.1 INTRODUCTION . . 113 .
7.2 THE ALGEBRAS A, A, A' AND J\F(A)" INTERACT 116 7.3 PROPERTIES OF THE
PUKANSZKY INVARIANT . . .' 120 7.4 THE PUKANSZKY INVARIANT IN GROUP
FACTORS . .,. .,*.,: * * . 123 7.5 EXAMPLES OF THE PUKANSZKY
INVARIANT 130 7.6 OPEN PROBLEMS 136 8 OPERATORS IN L[0,L]B(I/) . .
'137 8.1 INTRODUCTION .**;* .*:. . . . :. . . 137 8.2 MATRIX
COMPUTATIONS ; . . .*.". . . 137 8.3 MAIN RESULTS . . . . . . . . K .
. . . 141 9 PERTURBATIONS 148 * 9.1 INTRODUCTION V-.-Y. . . :.'.' .'. :
: . . . . 148 ; 9.2 AVERAGING ES OVER A . . ' . " . . . . . . 150 9.3
PERTURBING SUBALGEBRAS IN THE UNIFORM NORM . . *'*"*.* * *""*'* * * 156
9.4 LEMMAS ON CLOSE SUBALGEBRAS : . .'*:''. .'. . . . . . ."'. '. '.
.'. . . 159 9.5 DISTANCES AND GROUPOID HORMAIISERS . . . . . . . '.,'".
. . . . . . . . .174 9.6 NUMERICAL CONSTANTS FOR PERTURBATIONS '.'. . .
. . . '. . .' . .'.'. .''. 176 9.7 PERTURBATIONS OF MASAS BY AVERAGING .
. . . . . . . . .''.'.'.,. .'.' 183 10 GENERAL PERTURBATIONS '' ! '' '"
186 . 10.1 INTRODUCTION . ( . . , . . . . 186 10.2 THE JONES
INDEX .". .' . . .".',',,*. . . 186 10.3 CONTAINMENT OF FINITE
ALGEBRAS ,. 189 10.4 CLOSE VON NEUMANN ALGEBRAS . H . . . .,. . .,
193 11 SINGULAR MASAS . . ,-. 198 11.1 INTRODUCTION . . * . . . . . . .
: . ' . . . / 198 :* 11.2 BASIC LEMMAS . !; . .;.,.;, . : .-. .-. .
.-.-*;. .,;.:-;. 200 11.3 SINGULAR TO WAHP .,.,. : . I, . .I.
.,.203 11.4 A BASIS CONDITION FOR SINGULARITY . . . . . ; . . . . ;
.-. : . . . 208 11.5 ENUMERATION OF WORDS IN F2 . . . . . . .
.*.:.*.*.-.*. J. 212 : 11.6 THE LAPLACIAN MASA *.-. : .- *:.- .
.:.*. : . . . 218 CONTENTS VII 12 EXISTENCE OF SPECIAL MASAS 223
12.1 INTRODUCTION . . , 223 12.2 APPROXIMATIONS IN SUBALGEBRAS 224 12.3
CONSTRUCTING SEMIREGULAR MASAS 229 12.4 CONSTRUCTING SINGULAR MASAS 232
12.5 SINGULARITY AND AUTOMORPHISMS 239 13 IRREDUCIBLE HYPERFINITE
SUBFACTORS 242 13.1 INTRODUCTION 242 13.2 IRREDUCIBLE HYPERFINITE
SUBFACTORS EXIST 242 13.3 CARTAN MASAS IN HYPERFINITE SUBFACTORS 246
13.4 PROPERTY F 248 13.5 IRREDUCIBLE HYPERFINITES IN F FACTORS 253 14
MAXIMAL INJECTIVE SUBALGEBRAS 257 14.1 INTRODUCTION 257 14.2 MAXIMAL
INJECTIVITY AND MASAS 258 14.3 MAXIMAL INJECTIVITY OF SUBFACTORS 263 15
MASAS IN NON-SEPARABLE FACTORS 268 15.1 INTRODUCTION 268 15.2 MASAS IN
TV" 268 15.3 MASAS IN L(F S ) 275 16 SINGLY GENERATED HI FACTORS 278
16.1 INTRODUCTION 278 16.2 NOTATION AND DEFINITIONS 279 16.3 EXAMPLES
AND BASIC LEMMAS 283 16.4 THE SCALING FORMULA FOR Q 289 16.5
INTERPOLATED FREE GROUP FACTORS AND Q 296 16.6 SINGLE GENERATION 298
16.7 MAIN TECHNICAL LEMMAS 302 16.8 EXAMPLES OF SINGLY GENERATED HI
FACTORS 311 A THE ULTRAPOWER AND PROPERTY F 316 A.I INTRODUCTION 316 A.2
ULTRAFILTERS AND CHARACTERS 317 A.3 MAXIMAL QUOTIENTS OF FINITE ALGEBRAS
319 A.4 THE ALGEBRA N% 325 A.5 THE ULTRAPOWER N U 328 A.6 RELATIVE
COMMUTANTS IN TV" 334 A.7 PROPERTY F. REVISITED 337 VIII CONTENTS B
UNBOUNDED OPERATORS 342 B.I INTRODUCTION 342 B.2 BASIC RESULTS . 342 B.3
THE FUNCTIONAL CALCULUS ' 348 B.4 OPERATORS FROM L 2 (N) 359 B.5
OPERATORS FROM L^N) 362 C THE TRACE REVISITED 373 C.I INTRODUCTION 373
C.2 PRELIMINARY LEMMAS 373 C.3 CONSTRUCTION OF THE TRACE 375
BIBLIOGRAPHY 379 INDEX 394 INDEX OF SYMBOLS 398 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:29:27Z |
| indexdate | 2024-07-09T21:18:09Z |
| institution | BVB |
| isbn | 9780521719193 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016598684 |
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| physical | VIII, 400 S. |
| publishDate | 2008 |
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| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | London Mathematical Society lecture note series |
| series2 | London Mathematical Society lecture note series |
| spelling | Sinclair, Allan M. Verfasser aut Finite von Neumann algebras and masas Allan M. Sinclair ; Roger R. Smith 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2008 VIII, 400 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society lecture note series 351 Algèbres de Von Neumann Von Neumann, Algèbres de ram VonNeumann-Algebra (DE-588)4388395-3 gnd rswk-swf VonNeumann-Algebra (DE-588)4388395-3 s DE-604 Smith, Roger R. Verfasser aut London Mathematical Society lecture note series 351 (DE-604)BV000000130 351 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016598684&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sinclair, Allan M. Smith, Roger R. Finite von Neumann algebras and masas London Mathematical Society lecture note series Algèbres de Von Neumann Von Neumann, Algèbres de ram VonNeumann-Algebra (DE-588)4388395-3 gnd |
| subject_GND | (DE-588)4388395-3 |
| title | Finite von Neumann algebras and masas |
| title_auth | Finite von Neumann algebras and masas |
| title_exact_search | Finite von Neumann algebras and masas |
| title_exact_search_txtP | Finite von Neumann algebras and masas |
| title_full | Finite von Neumann algebras and masas Allan M. Sinclair ; Roger R. Smith |
| title_fullStr | Finite von Neumann algebras and masas Allan M. Sinclair ; Roger R. Smith |
| title_full_unstemmed | Finite von Neumann algebras and masas Allan M. Sinclair ; Roger R. Smith |
| title_short | Finite von Neumann algebras and masas |
| title_sort | finite von neumann algebras and masas |
| topic | Algèbres de Von Neumann Von Neumann, Algèbres de ram VonNeumann-Algebra (DE-588)4388395-3 gnd |
| topic_facet | Algèbres de Von Neumann Von Neumann, Algèbres de VonNeumann-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016598684&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000130 |
| work_keys_str_mv | AT sinclairallanm finitevonneumannalgebrasandmasas AT smithrogerr finitevonneumannalgebrasandmasas |