Building/Location: Sidney Smith (Room: 2114)

Abstract:

Given a non-unital non-commutative C*-algebra A, we give some partial answers to the question whether it is possible to lift an infinite family of positive orthogonal elements in the corona algebra C(A) to a set of positive commuting elements in the multiplier algebra M(A). While this is true for countable families in the Calkin algebra, this is not the case in general for uncountable families. We prove, for A separable and primitive, that there exists a family of aleph_1 orthogonal positive commuting elements in C(A) containing no uncountable subset which simultaneously lifts to a commutative family in M(A).