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Proceedings of the American Mathematical Society

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

 

 

A note on cocycles of unitary representations


Authors: W. Parry and K. Schmidt
Journal: Proc. Amer. Math. Soc. 55 (1976), 185-190
DOI: https://doi.org/10.1090/S0002-9939-1976-0393336-0
MathSciNet review: 0393336
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Abstract: Given a unitary representation $ U$ of a locally compact abelian group $ G$, we investigate the relationship between two cocycles $ {a_1},{a_2}:V{a_1} = {a_2} + b$ for some unitary operator $ V$ commuting with $ U$ and some coboundary $ b$. A necessary and sufficient condition is given in terms of canonical-finite measures defined on $ G - 1$. These results are applied to the representation of $ Z$ defined by the shift of a stationary Markov chain.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0393336-0
Keywords: Unitary representations, cocycles, coboundaries
Article copyright: © Copyright 1976 American Mathematical Society