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)
Original language | English |
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Journal | Expositiones Mathematicae |
Volume | 34 |
Issue number | 1 |
Pages (from-to) | 27–42 |
ISSN | 0723-0869 |
DOIs | |
Publication status | Published - 2016 |
ID: 148641587