Classification of certain order zero c.p. maps by traces

Yasuhiko Sato  (Kyoto University)

10:00 am to 11:00 am, Mar 20th, 2015   A1510, Science Building

Abstract:

Order zero c.p. maps were systematically studied by W. Winter and J. Zacharias, based on the previous work by M. Wolf. These are c.p. maps preserving orthogonality, they are particularly well-behaved. In this talk, we introduce a classification of certain order zero c.p. maps up to approximate unitary equivalence by their behavior on tracial states. As an application of this classification, it was shown that the nuclear dimension of unital separable simple amenable $\mathcal{Z}$-absorbing $\mathrm{C}^*$-algebra is at most one if its extreme boundary of trace space is compact.

This is a joint work with J. Bosa, N. P. Brown, A. Tikuisis, S. White, and W. Winter.