Operator Algebras: Theory of C*-Algebras and Von Neumann Algebras, Volume 13

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Taylor & Francis, 2006 - Mathematics - 517 pages
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This volume attempts to give a comprehensive discussion of the theory of operator algebras (C*-algebras and von Neumann algebras. ) The volume is intended to serve two purposes: to record the standard theory in the Encyc- pedia of Mathematics, and to serve as an introduction and standard reference for the specialized volumes in the series on current research topics in the subject. Since there are already numerous excellent treatises on various aspects of thesubject,howdoesthisvolumemakeasigni?cantadditiontotheliterature, and how does it di?er from the other books in the subject? In short, why another book on operator algebras? The answer lies partly in the ?rst paragraph above. More importantly, no other single reference covers all or even almost all of the material in this volume. I have tried to cover all of the main aspects of “standard” or “clas- cal” operator algebra theory; the goal has been to be, well, encyclopedic. Of course, in a subject as vast as this one, authors must make highly subjective judgments as to what to include and what to omit, as well as what level of detail to include, and I have been guided as much by my own interests and prejudices as by the needs of the authors of the more specialized volumes.
 

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Contents

I
1
II
2
III
3
IV
4
V
5
VIII
6
IX
7
X
8
XCV
187
XCVI
190
XCVII
191
XCVIII
192
XCIX
193
C
197
CI
199
CII
205

XI
9
XII
10
XIII
13
XV
14
XVI
17
XVII
18
XVIII
19
XXI
20
XXII
21
XXIII
23
XXV
25
XXVI
27
XXVIII
29
XXIX
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XXX
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XXXI
36
XXXIII
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XXXV
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XXXVI
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XXXVII
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XXXVIII
44
XXXIX
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XLI
48
XLII
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XLIII
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XLIV
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XLVI
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XLVII
57
XLVIII
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XLIX
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L
61
LI
63
LII
67
LIII
72
LIV
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LV
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LVII
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LVIII
82
LX
83
LXI
85
LXII
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LXIII
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LXIV
95
LXV
100
LXVI
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LXVII
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LXVIII
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LXIX
107
LXX
111
LXXI
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LXXII
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LXXIII
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LXXIV
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LXXV
132
LXXVI
137
LXXVIII
141
LXXIX
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LXXX
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LXXXI
149
LXXXII
150
LXXXIII
154
LXXXV
156
LXXXVI
158
LXXXVII
167
LXXXVIII
176
LXXXIX
179
XC
180
XCII
182
XCIII
184
XCIV
186
CIII
211
CIV
212
CVI
214
CVII
221
CVIII
222
CIX
225
CX
227
CXI
231
CXII
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CXIII
237
CXIV
240
CXV
243
CXVI
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CXVII
245
CXVIII
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CXIX
257
CXX
259
CXXI
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CXXII
269
CXXIII
275
CXXV
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CXXVI
288
CXXVII
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CXXVIII
293
CXXX
295
CXXXII
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CXXXIII
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CXXXIV
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CXXXV
306
CXXXVI
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CXXXVII
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CXXXVIII
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CXXXIX
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CXL
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CXLI
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CXLII
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CXLIII
337
CXLIV
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CXLV
344
CXLVI
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CXLVII
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CXLVIII
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CXLIX
360
CL
362
CLI
365
CLII
367
CLIV
368
CLVI
374
CLVII
378
CLVIII
383
CLIX
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CLX
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CLXII
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CLXIII
402
CLXIV
408
CLXV
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CLXVI
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CLXVII
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CLXIX
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CLXX
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CLXXI
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CLXXII
444
CLXXIII
445
CLXXIV
452
CLXXV
457
CLXXVII
460
CLXXVIII
464
CLXXIX
479
CLXXX
505
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Page 479 - REFERENCES [ 1 ] H. ARAKI, A lattice of von Neumann algebras associated with the quantum, theory of a free Bose field, J.
Page 503 - A proof of Tomita's fundamental theorem in the theory of standard von Neumann algebras".

About the author (2006)

Blackadar-University of Nevada, Reno