Descriptive properties of measure preserving actions and the associated unitary representations
This thesis consists of two independent parts.
In the first part, we study the descriptive complexity of full groups [E]. The main result is
i) If E is not smooth, then [E] is Sigma^0_3 complete;
ii) If E is smooth, then [E] is closed.
In the second part, we study descriptive properties of the Koopman unitary repreesentation associated with the measure preserving action. We characterize the smoothness and compressibility of the equivalence induced by the unitary representaion. We also study many connections between the equivalence relation on L^2(X) and the equivalence relation on X.
Advisor:A.S. Kechris; David Wales; Nikolai G. Makarov
School:California Institute of Technology
School Location:USA - California
Source Type:Master's Thesis
Date of Publication:05/12/2005