On weakly D-differentiable operators

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Let DD be a self-adjoint operator on a Hilbert space HH and aa a bounded operator on HH. We say that aa is weakly DD-differentiable, if for any pair of vectors ξ,ηξ,η from HH the function 〈eitDae−itDξ,η〉〈eitDae−itDξ,η〉 is differentiable. We give an elementary example of a bounded operator aa, such that aa is weakly DD-differentiable, but the function eitDae−itDeitDae−itD is not uniformly differentiable. We show that weak  DD-differentiability   may be characterized by several other properties, some of which are related to the commutator (Da−aD)
TidsskriftExpositiones Mathematicae
Udgave nummer1
Sider (fra-til)27–42
StatusUdgivet - 2016

ID: 148641587