Bounded perturbations of the Heisenberg commutation relation via dilation theory

We extend the notion of dilation distance to strongly continuous one-parameter unitary groups. If dilation distance between two such groups is finite, then these can be represented on same space in a way that their generators have domain and are fact bounded perturbation one another. This result extends d d -tuples apply our results Weyl canonical commutation relations, as special case we recover Haagerup Rørdam [Duke Math. J. 77 (1995), pp. 627–656 ] infinite ampliation position momentum operators satisfying Heisenberg relation pair commuting selfadjoint operators. also Gao’s higher-dimensional generalization Rørdam’s result, typical cases significantly improve control bound when dimension grows.