Operator Algebra Seminar by Yasuhiko Sato

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

Abstract: A completely positive map is called order zero if it preserves orthogonality. Recent developments in the classification theorem of C*-algebras suggest that order zero c.p. maps are very compatible with projectionless 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 C*-algebras with a unique tracial state. This talk is based on a joint work with Stuart White and Wilhelm Winter.