Lethbridge Number Theory and Combinatorics Seminar: Alexey Popov

An algebra is a vector space with a well-defined multiplication. An operator algebra is an algebra of operators acting on a Hilbert space, typically assumed closed in the norm topology. An easy example of an operator algebra is the algebra M_n(C) of all the complex nxn matrices.

In this colloquium-style talk, we will discuss operator algebras A with the following property: every A-invariant subspace is complemented by another A-invariant subspace. This property is called the Reduction property and is a kind of semisimplicity. We will discuss the connections of this property to some classical problems, such as Kadison Similarity Problem and the structure of amenable operator algebras.