Christopher Felder: Units for Forward Operator Monoids

Abstract.

This talk will introduce a forward operator monoid— a discrete collection of bounded linear operators acting on a separable Hilbert space, which contains the identity, and has a strict monoid structure. We will then discuss generalized inner and cyclic vectors for these monoids, with a focus on vectors which are both inner a cyclic, which we will call units. Time permitting, we will connect this to some interesting open problems in analysis, including some completeness and approximation problems.