|Time:|| 12:00 - 13:20
PPB 300 (next to Facilities Management Services)
C-star algebras and set theory II
We will continue last week's talk with some basic structural results on C-star algebras, leading into the Gelfand-Naimark theorem on abelian C-star algebras; a particular instance of this will give us the continuous functional calculus, a major tool in the theory. Then we will go into the representation theory of C-star algebras, ending with the GNS construction, which represents an arbitrary C-star algebra (faithfully) as an algebra of operators on some Hilbert space. Time permitted, we will talk about Naimark's problem, an old question in representation theory which was partially solved recently (with the use of diamond) by Akemann and Weaver.