M. B. Bekka, N. Louvet (auth.), Joachim Cuntz, Siegfried's C*-Algebras: Proceedings of the SFB-Workshop on C*-Algebras, 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 booklet incorporates a number of articles supplied by means of the members 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 college of Münster, Germany. the purpose of the workshop used to be to compile top 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 members. there have been 19 one-hour lectures on quite a few subject matters like - class of nuclear C* -algebras, - common K-theory for C* -algebras, - distinctive C* -algebras and certain teams, - C*-algebras linked to (infinite) matrices and C*-correspondences, - noncommutative prob skill concept, - deformation quantization, - staff C* -algebras and the Baum-Connes conjecture, giving a large assessment of the newest 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 belief of publishing the court cases of the convention. There are primarily sorts of contributions. On one aspect there are a number of articles giving surveys and overviews on new advancements and im­ portant result of the speculation, at the different facet one unearths unique articles with attention-grabbing new results.

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E) 1/ A and Bare MF algebras, then A @a B is an MF algebra tor some cross norm 0:. o/ them is nuclear, then A @ B = A @min B is an MF algebra. (f) 1/ A is MF, then every separable C*-algebra strong Morita equivalent to Ais MF. (g) Let (B(t)) be a continuous field 0/ separable C*-algebras over NU {oo}. 1/ each B(t) tor tE N is an MF algebra, then B(oo) is an MF algebra. (h) Let (An) be a sequence 0/ MF algebras. 1 An) is an MF algebra. (i) Let (An,

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. So A can be embedded as a C*-subalgebra of a strong NF algebra B with a retraction (homomorphic conditional expectation) from B onto A. Thus, in particular, a nudear C* -sub algebra of a strong NF algebra need not be strong NF. 1(ix) that the dass of strong NF algebras is dosed under stable isomorphism (strong Morita equivalence). 9. 17} A tensor product of strong NF algebras is strong NF.

5]. 5 NF Algebras We now describe the structure of NF algebras. Of course, every NF algebra is an MF algebra. The key observation in developing the further properties of NF algebras is that NF algebras are also nuclear. ) Nuclearity of NF algebras then follows from the next simple construction. 1. Every NF algebra is a quotient of a strong NF algebra. Proof. Let (An, cPm,n) be an NF system for an NF algebra A, and for each n let B n = Al EB· .. EB An, 'l/Jn,n+l : B n -t B n+l defined by 'l/Jn,n+l (Xl, ...

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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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