BOUNDED PERTURBATIONS OF THE HEISENBERG COMMUTATION RELATION VIA DILATION THEORY
Peer reviewed, Journal article
Accepted version
Date
2023Metadata
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- Institutt for matematiske fag [2531]
- Publikasjoner fra CRIStin - NTNU [38672]
Original version
Proceedings of the American Mathematical Society. 2023, 151 (9), 3949-3957. 10.1090/proc/16456Abstract
We extend the notion of dilation distance to strongly continuous one-parameter unitary groups. If the dilation distance between two such groups is _nite, then these groups can be represented on the same space in such a way that their generators have the same domain and are in fact a bounded perturbation of one another. This result extends to d-tuples of one-parameter unitary groups. We apply our results to the Weyl canonical commutation relations, and as a special case we recover the result of Haagerup and R_rdam that the in_nite ampliation of the canonical position and momentum operators satisfying the Heisenberg commutation relation are a bounded perturbation of a pair of strongly commuting selfadjoint operators. We also recover Gao’s higher-dimensional generalization of Haagerup and R_rdam’s result, and in typical cases we signi_cantly improve control of the bound when the dimension grows.