Free entropy dimensions and approximate liftings

<p>In the first chapter of the dissertation, we give a very elementary proof of a more detailed version of one of D. Voiculescu's results, which was a key ingredient in Voiculescu's proof that his free entropy is additive when the variables are free.</p><p>In the second chapter of the dissertation, based on the notion of upper free orbit-dimension introduced by D. Hadwin and J. Shen, we introduce a new invariant on finite von Neumann algebras that do not necessarily act on separable Hilbert space. We show that this invariant is independent of the generating set, and we obtain a number of results for von Neumann algebras that are not finitely generated.</p><p>In the third chapter of the dissertation, we consider the class of approximately divisible C*-algebras. Let A be a separable unital approximately divisible C*-algebra. We show that A is generated by two self-adjoint elements and the topological free entropy dimension of any finite generating set of A is less than or equal to 1. In addition, we show that the similarity degree of A is at most 5.</p><p>In the fourth chapter of the dissertation, we show that two (weakly) semiprojective unital C*-algebras, each generated by n projections, can be glued together with partial isometries to define a larger (weakly) semiprojective algebra. In the von Neumann algebra setting, we prove lifting theorems for trace-preserving *-homomorphisms from abelian von Neumann algebras or hyperfinite von Neumann algebras into ultraproducts. We also extend and simplify a classical result of S. Sakai by showing that a tracial ultraproduct of C*-algebras is a von Neumann algebra.</p>

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Dissertation

Year

2008

Author dc:creator

• Li, Weihua

Contributors dc:contributor

• Don Hadwin

• Mathematics

Repository record dc:identifier

https://scholars.unh.edu/dissertation/478

OAI identifier oai:identifier

oai:scholars.unh.edu:dissertation-1477