Von Neumann AlgebrasElsevier, 18 août 2011 - 478 pages In this book, we study, under the name of von Neumann algebras, those algebras generally known as “rings of operators“ or “W*-algebras.“ The new terminology, suggested by J. Dieudonng, is fully justified from the historical point of view. Certain of the results are valid for more general algebras. We have, however systematically avoided this kind of generalization, except when it would facilitate the study of von Neumann algebras themselves. Parts I and I1 comprise those results which at present appear to’be the most useful for applications, although we do not embark on the study of those applications. Part 111, which is more technical, is primarily intended for specialists; it is virtually independent of Part 11. |
Table des matières
REDUCTION OF VON NEUMANN ALGEBRAS | 159 |
FURTHER TOPICS | 241 |
APPENDIX I | 359 |
APPENDIX II | 363 |
APPENDIX III | 365 |
APPENDIX IV | 367 |
APPENDIX V | 371 |
SOME REMARKS CONCERNING THE TERMINOLOGY | 377 |
| 381 | |
| 384 | |
REFERENCES | 389 |
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Expressions et termes fréquents
abelian von Neumann algebra in H Amer automorphism bounded canonical central support centre chapter commutes complex Hilbert space continuous linear continuous linear form converges strongly corollary countable cyclic defined denote dense discrete disjoint projections elements of H equivalent everywhere exists factor of type field Q finite factor finite von Neumann function Gelfand isomorphism hence hermitian Hilbert algebra homomorphism hyperfinite factor lemma Let H Let Q linear mapping linear subspace locally compact locally compact space measurable field measurable vector fields Moreover necessary and sufficient negligible set Neumann alge Neumann algebra norm normal positive linear O—finite operator algebras pairwise disjoint partial isometry polar decomposition positive linear form Proc Proof properly infinite proposition purely infinite semi—finite sequence Show subset Suppose supremum tensor product theorem tion topology trace on A+ two—sided ideal ultra—strongly unit ball unitary operator V—measurable von Neumann algebra W*—algebras weak topology whence