Wei, Tzer-jen (2005) Descriptive properties of measure preserving actions and the associated unitary representations. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-05202005-160741
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.
|Item Type:||Thesis (Dissertation (Ph.D.))|
|Subject Keywords:||descriptive set theory; ergodic Theory; unitary representations|
|Degree Grantor:||California Institute of Technology|
|Division:||Physics, Mathematics and Astronomy|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||12 May 2005|
|Author Email:||tzerjen (AT) caltech.edu|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||23 May 2005|
|Last Modified:||26 Dec 2012 02:43|
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