Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4582352 | Expositiones Mathematicae | 2016 | 16 Pages |
Abstract
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)(Da−aD).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Erik Christensen,