Murray-von Neumann equivalence for positive elements and order zero c.p. maps

Yasuhiko Sato  (Kyoto University; University of Copenhagen)

10:00 am to 11:00 am, Apr 14th, 2014   Science Building A1510

Abstract:

A completely positive map is called order zero if it preserves orthogonality. Recent developments in the classification theorem of $\mathrm{C}^*$-algebras suggest that order zero c.p. maps are very compatible with projectionless $\mathrm{C}^*$-algebras. In this talk, we investigate the Murray--von Neumann equivalence for positive elements and see that it plays a crucial role for the understanding of order zero c.p. maps and their conjugacy classes. As a consequence of this study, we obtain an affirmative answer to the Toms and Winter conjecture for $\mathrm{C}^*$-algebras with a unique tracial state.

This talk is based on a joint work with Stuart White and Wilhelm Winter.