FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 8, PAGES 193-212

**On isomorphity of measure-preserving
$$****Z**^{2}-actions that have
isomorphic Cartesian powers

A. E. Troitskaya

Abstract

View as HTML
View as gif image

Assume that $$D and $$P are representations
of the group $$**Z**^{2} by
operators on the space $L$_{2}(X, m) that are induced by
measure-preserving automorphisms, and for some $d$, the representations
$$D^{Äd}
and $$P^{Äd}
are conjugate to each other, $$D (**Z**^{2}
\ (0,0)) consists of weakly mixing operators, and
there is a weak limit (over some subsequence in $$**Z**^{2} of
operators from $$D
(**Z**^{2})) which is equal to
a nontrivial, convex linear combination of elements of
$$D
(**Z**^{2}) and of the projection onto
constant functions.
We prove that in this case, $$D and $$P are also conjugate to
each other.

Location: http://mech.math.msu.su/~fpm/eng/k07/k078/k07812h.htm

Last modified: June 13, 2008