Title: Dilations of symmetric operators shifted by a unitary group
Abstract: Let Q be a symmetric operator and Ux a one parameter unitary group in a Hilbert space such that Ux dom Q ⊂ dom Q and UxQUx∗ ϑ = Qϑ + xϑ for ϑ ϵ dom Q. It is shown by a compactness argment that Q admits a resolution Q = ∝ xF[dx] with a positive operator valued measure satisfying UxF[σ]Ux∗ = F[σ + x]. This entails the existence of a selfadjoint extension of Q to a larger space satisfying the analogus commutation relation with a suitable extended unitary group. This result is generalized to n commuting symmetric operators transformed among each other by a representation of an amenable subgroup of the affine group in Rn.
Publication Year: 1990
Publication Date: 1990-08-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 13
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