Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series A, Pt. 3, pp.307--317

JOINING PROPERTIES OF ERGODIC DYNAMICAL SYSTEMS HAVING SIMPLE SPECTRUM

By

GEOFFREY R. GOODSON, Towson University, MD, USA

SUMMARY. It was shown in Goodson (1995) that if T is an ergodic automorphism having simple spectrum and defined on a standard Borel probability space for which T and T -1 are isomorphic, i.e., there is an automorphism S satisfying ST=T-1S, then S 2=I, the identity automorphism. If T and T-1 are not isomorphic, we can no longer consider conjugations but rather joinings of T and T-1. It is shown that if P is a joining (Markov intertwining) between T and T-1, then P is self--adjoint. Applications of the methods are given to provide new proofs of some well know results.

AMS (1991) subject classification. 28D05, 37A30, 47A35.

Key words and phrases. Simple spectrum, joining, Markov intertwining.

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