ON THE SUPERRIGIDITY OF MALLEABLE ACTIONS WITH SPECTRAL GAP

摘要

Some of the most interesting aspects of the dynamics of measure preserving actions of countable groups on probability spaces, (X, μ), are revealed by the study of group measure space von Neumann algebras ([MvN1]) and the classification of actions up to orbit equivalence (OE), i.e. up to isomorphism of probability spaces carrying the orbits of actions onto each other. Although one is in von Neumann algebras and the other in ergodic theory, the two problems are closely related, as an OE of actions has been shown to implement an algebra isomorphism taking onto , and vice-versa ([Si], [Dy], [FM]). In particular, the isomorphism class of only depends on the equivalence relation .