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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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


Author: A. E. Nussbaum
Journal: Trans. Amer. Math. Soc. 152 (1970), 419-429
MSC: Primary 47.50
MathSciNet review: 0268719
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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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DOI: https://doi.org/10.1090/S0002-9947-1970-0268719-9
Keywords: Symmetric operators, Hilbert space, semigroup, unbounded operators, spectral representation
Article copyright: © Copyright 1970 American Mathematical Society