Kaplansky Density for automorphism groups

Matt Daws (University of Central Lancashire)

Thursday 9th May 16:00-17:00 Maths 311B

Abstract

We will discuss the Kaplansky Density result for operator algebras, and its failure for non-self-adjoint algebras. We will then turn our attention to automorphism groups of operator algebras, and in particular their "analytic generators". We will show that a Kaplansky Density type result holds for such generators: when we have an automorphism group of a von Neumann algebra which restricts to a sigma-weakly dense C*-subalgebra, the analytic generator of the C*-algebra group is sigma-weakly dense in that for the von Neumann algebra. This setup occurs in the theory of locally compact quantum groups, in particular, when the antipode is unbounded.

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