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

Abstract
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.

Acknowledgements

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
jmh@math.unc.edu
http://www.math.unc.edu/Faculty/jhawkins/

Cesar E. Silva:
Math Department, Williams College, Williamstown, MA 02167
Cesar.E.Silva@williams.edu
http://www.williams.edu/Mathematics/csilva/