By M. B. Bekka, N. Louvet (auth.), Joachim Cuntz, Siegfried Echterhoff (eds.)
This ebook incorporates a number of articles supplied by way of the members of the SFB-workshop on C*-algebras, March eight - March 12, 1999 which used to be held on the Sonderforschungsbereich "Geometrische Strukturen in der reinen Mathematik" of the college of Münster, Germany. the purpose of the workshop was once to assemble major specialists within the thought of C* -algebras with promising younger researchers within the box, and to supply a stimulating surroundings for discussions and interactions among the individuals. there have been 19 one-hour lectures on a variety of issues like - class of nuclear C* -algebras, - basic K-theory for C* -algebras, - targeted C* -algebras and distinctive teams, - C*-algebras linked to (infinite) matrices and C*-correspondences, - noncommutative prob skill idea, - deformation quantization, - crew C* -algebras and the Baum-Connes conjecture, giving a large evaluate of the newest advancements within the box, and serving as a foundation for discussions. We, the organizers of the workshop, have been tremendously proud of the distinction of the lectures and so have been ended in the assumption of publishing the complaints of the convention. There are primarily different types of contributions. On one part there are a number of articles giving surveys and overviews on new advancements and im portant result of the idea, at the different part one unearths unique articles with attention-grabbing new results.
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Extra info for C*-Algebras: Proceedings of the SFB-Workshop on C*-Algebras, Münster, Germany, March 8–12, 1999
Sample text
13] a unital representation 'Y : A -+ M(K 0 B) is unitally absorbing if and only if
4), hence (3){:? 1. The latter equivalence was conjectured informally by Lin [L], and it was known to be true if Ais abelian [D I ], or if A can be approximated by nuclear C*-subalgebras satisfying the UCT and having finitely generated K-theory and B is simple [L], or if A is simple and B satisfies certain conditions in unstable K-theory and has bounded exponential rank [L], [DEI]' The proof of (3) {:? 11. Unlike previous approaches, the proof does not use the theorem of Kadison and Ringrose on derivable automorphisms of C*-algebras.
Every separable nuclear C*-algebra is a quotient of a strong NF algebra. 5. 1(ix). C* (S EB SO) is also NF but not strong NF far the same reason. 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.