A non-commutative notion of separate continuity

Speaker: M. Daws, (Leeds)

Date: Tuesday, November 25th

Time: 4:00pm

Location: Trinity College Dublin, TCD WR20

Abstract:
The classical Gelfand theory of communicate C*-algebras tells us that communicate C*-algebras are nothing but the algebras C_0(K), the algebra of complex valued functions, vanishing at infinity, on a locally compact Hausdorff space. This, in some sense, is the motivating example behind non-commutative geometry / topology. How might we similarly consider separate continuity from a C*-algebra framework? We present one way to do this-- the naive "noncommutative" definition thus resulting doesn't quite work, but we will show that while our candidate set is not an algebra, in general, it does always contain a "maximum" C*-subalgebra. Time allowing, I will present some applications to the study of "quantum" topological semigroups.

Series: Ananlysis