A note on cocycles of unitary representations
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- by W. Parry and K. Schmidt PDF
- Proc. Amer. Math. Soc. 55 (1976), 185-190 Request permission
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.References
- Robin Fellgett and William Parry, Endomorphisms of a Lebesgue space. II, Bull. London Math. Soc. 7 (1975), 151–158. MR 382590, DOI 10.1112/blms/7.2.151
- Frederick P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1969. MR 0251549
- K. R. Parthasarathy and K. Schmidt, Positive definite kernels, continuous tensor products, and central limit theorems of probability theory, Lecture Notes in Mathematics, Vol. 272, Springer-Verlag, Berlin-New York, 1972. MR 0622034
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 55 (1976), 185-190
- DOI: https://doi.org/10.1090/S0002-9939-1976-0393336-0
- MathSciNet review: 0393336