Operator algebra seminar

Speaker: Erik Christensen, University of Copenhagen

Title: On weakly D-differentiable operators

Abstract:  Let D be a self-adjoint operator on a Hilbert space H and b a bounded operator on H. We say that b is weakly D-differentiable, if for any pair of vectors x, y from H the function < exp(itD) b exp(-itD) x, y> is differentiable. We give an elementary example of a bounded operator b such that b is weakly D-differentiable, but exp(itD) b exp(-itD) is not uniformly differentiable.

We show that weak D-differentiability of a bounded operator b may be characterized by several other properties, some of which are related to properties of the commutator [D,b] = Db - bD.