Place: Bahen Centre Information (Room BA 2165)
Date: June 8, 2018 (13:30-15:00)
Speaker: Andrea Vaccaro
Title: Embedding C*-algebras into the Calkin algebra
Given a separable Hilbert space H, the Calkin algebra is the quotient C(H) = B(H)/K(H), B(H) being the algebra of all linear continuous operators from H into itself, and K(H) the closed ideal of compact operators. The Calkin algebra can be considered a noncommutative analogue of P(omega)/Fin, and it is known that these two objects share many structural properties. We show that yet another property of P(omega)/Fin has a noncommutative analogue for C(H). In particular, it is known that for every poset P there is a ccc poset H_P which forces the existence of an embedding of P into P(omega)/Fin. We prove that for any C*-algebra A there exists a ccc poset which forces the existence of an embedding of A into C(H).