On weakly D-differentiable operators
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On weakly D-differentiable operators. / Christensen, Erik.
In: Expositiones Mathematicae, Vol. 34, No. 1, 2016, p. 27–42.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - On weakly D-differentiable operators
AU - Christensen, Erik
PY - 2016
Y1 - 2016
N2 - 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)
AB - 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)
U2 - 10.1016/j.exmath.2015.03.002
DO - 10.1016/j.exmath.2015.03.002
M3 - Journal article
VL - 34
SP - 27
EP - 42
JO - Expositiones Mathematicae
JF - Expositiones Mathematicae
SN - 0723-0869
IS - 1
ER -
ID: 148641587