Download C*-Algebras: Proceedings of the SFB-Workshop on C*-Algebras, by M. B. Bekka, N. Louvet (auth.), Joachim Cuntz, Siegfried PDF

By M. B. Bekka, N. Louvet (auth.), Joachim Cuntz, Siegfried Echterhoff (eds.)

ISBN-10: 3540675620

ISBN-13: 9783540675624

ISBN-10: 364257288X

ISBN-13: 9783642572883

This e-book features a selection of articles supplied by means of the contributors of the SFB-workshop on C*-algebras, March eight - March 12, 1999 which was once held on the Sonderforschungsbereich "Geometrische Strukturen in der reinen Mathematik" of the collage of Münster, Germany. the purpose of the workshop used to be to assemble prime specialists within the conception of C* -algebras with promising younger researchers within the box, and to supply a stimulating surroundings for discussions and interactions among the contributors. there have been 19 one-hour lectures on numerous issues like - class of nuclear C* -algebras, - common K-theory for C* -algebras, - distinctive C* -algebras and precise teams, - C*-algebras linked to (infinite) matrices and C*-correspondences, - noncommutative prob skill concept, - deformation quantization, - team C* -algebras and the Baum-Connes conjecture, giving a large review of the most recent advancements within the box, and serving as a foundation for discussions. We, the organizers of the workshop, have been drastically happy with the distinction of the lectures and so have been ended in the assumption of publishing the court cases of the convention. There are primarily types of contributions. On one aspect there are numerous articles giving surveys and overviews on new advancements and im­ portant result of the idea, at the different part one unearths unique articles with fascinating new results.

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Additional resources for C*-Algebras: Proceedings of the SFB-Workshop on C*-Algebras, Münster, Germany, March 8–12, 1999

Example text

If A is nonunital, we say A is finite [resp. stably finite] if its unitization A is finite [resp. stably finite]. 2. Let (An,

1(ix) that if A is separable and nuclear, then CA and S Aare strong NF if and only if Ais; thus, for example, S02 is NF but not strong NF. 6. 4} If A is separable, nuclear, and prime, then A is a strong NF algebra if and only if some (hence every) faithful irreducible representation of A is quasidiagonal. 7. Every antiliminal prime NF algebra is a strong NF algebra. Every simple NF algebra is a strong NF algebra. 8. Let A be any NF algebra, and let B be a split essential extension of A by OC. Then B is a strong NF algebra.

1; is dominated by 'Tr. If II is aset of irreducible representations of A, then 1; is dominated by II if 1; is dominated by some 'Tr EIl. 7. Let (B n ) be a sequence 0/ C*-algebras, and IIn a separating 0/ irreducible representations 0/ B n . Let A be a separable C*-subalgebra 0/ IL B n , k E N, and ljJ a pure completely positive map /rom A to M k . Then /or each n there is a pure completely positive map IjJn /rom B n to Mk, dominated by IIn , such that ljJ = lim w IjJn. /amily This lemma is a variant (generalization) of the fact that every pure state of A is a limit of vector states from any separating family of representations of A.

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C*-Algebras: Proceedings of the SFB-Workshop on C*-Algebras, Münster, Germany, March 8–12, 1999 by M. B. Bekka, N. Louvet (auth.), Joachim Cuntz, Siegfried Echterhoff (eds.)


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