On weakly D-differentiable operators

TY - JOUR

T1 - On weakly D-differentiable operators

AU - Christensen, Erik

PY - 2016

Y1 - 2016

N2 - 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).

AB - 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).

U2 - 10.1016/j.exmath.2015.03.002

DO - 10.1016/j.exmath.2015.03.002

M3 - Journal article

SN - 0723-0869

VL - 34

SP - 27

EP - 42

JO - Expositiones Mathematicae

JF - Expositiones Mathematicae

IS - 1

ER -