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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Stone's theorem for a group of unitary operators over a Hilbert space


Author: Habib Salehi
Journal: Proc. Amer. Math. Soc. 31 (1972), 480-484
MSC: Primary 47A60; Secondary 46G99
DOI: https://doi.org/10.1090/S0002-9939-1972-0300128-3
MathSciNet review: 0300128
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Abstract: The spectral representation for a group of unitary operators acting on a Hilbert space where the parameter set is a separable real Hilbert space is obtained. The usual spectral representation of such a group of unitary operators is when the parameter set is a locally compact abelian group (Stone's theorem). The main result used in the proof is the Bochner theorem on the representation of positive definite functions on a real Hilbert space.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0300128-3
Keywords: Group of unitary operators, spectral representation, Hilbert space, Hilbert-Schmidt operators, $ \tau $-topology, positive definite, stationary stochastic processes
Article copyright: © Copyright 1972 American Mathematical Society