文摘
Let D be a self-adjoint operator on a Hilbert space H and a a bounded operator on H. We say that a is weakly D-differentiable, if for any pair of vectors ξ,η from H the function 〈eitDae−itDξ,η〉 is differentiable. We give an elementary example of a bounded operator a, such that a is weakly D-differentiable, but the function eitDae−itD is not uniformly differentiable. We show that weak D-differentiability may be characterized by several other properties, some of which are related to the commutator (Da−aD).