Spectral representation of certain one-parametric families of symmetric operators in Hilbert space

Nussbaum, A. E.

doi:10.1090/S0002-9947-1970-0268719-9

Spectral representation of certain one-parametric families of symmetric operators in Hilbert space
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by A. E. Nussbaum PDF

Trans. Amer. Math. Soc. 152 (1970), 419-429 Request permission

Abstract:

It is proved that if a one-parameter family of symmetric operators acting in a Hilbert space has the semigroup property on a dense linear manifold and is weakly continuous, then the operators are essentially selfadjoint and permute in the sense of permuting spectral projections of the selfadjoint extensions. It follows from this that the operators have a joint spectral integral representation.

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