New York Journal of Mathematics
Volume 3A (1997-1998) 99-115


Jane Hawkins and Cesar E. Silva

Characterizing Mildly Mixing Actions by Orbit Equivalence of Products

Published: March 18, 1998
Keywords: mild mixing, amenable action, nonsingular endormorphism
Subject: 28D05, 28D99, 58F11

We characterize mildly mixing group actions of a noncompact, locally compact, second countable group G using orbit equivalence. We show an amenable action Φ of G is mildly mixing if and only if G is amenable and for any nonsingular ergodic G-action Ψ, the product G-action Φ×Ψ is orbit equivalent to Ψ. We extend the result to the case of finite measure preserving noninvertible endomorphisms, i.e., when G=N, and show that the theorem cannot be extended to include nonsingular mildly mixing endomorphisms.


The first author was supported in part by the IMA with funds provided by the NSF & NSF grant DMS# 9203489

The second author was partially supported by NSF grant DMS #9214077

Author information

Jane Hawkins:
Math Department, CB #3250, University of North Carolina, Chapel Hill, NC 27599

Cesar E. Silva:
Math Department, Williams College, Williamstown, MA 02167