UWSpace is currently experiencing technical difficulties resulting from its recent migration to a new version of its software. These technical issues are not affecting the submission and browse features of the site. UWaterloo community members may continue submitting items to UWSpace. We apologize for the inconvenience, and are actively working to resolve these technical issues.
 

On the Similarity of Operator Algebras to C*-Algebras

Thumbnail Image

Files

m2george2006.pdf (456 KB)

Date

2006

Authors

Georgescu, Magdalena

Journal Title

Journal ISSN

Volume Title

Publisher

University of Waterloo

Abstract

This is an expository thesis which addresses the requirements for an operator algebra to be similar to a <em>C</em>*-algebra. It has been conjectured that this similarity condition is equivalent to either amenability or total reductivity; however, the problem has only been solved for specific types of operators. <br /><br /> We define amenability and total reductivity, as well as present some of the implications of these properties. For the purpose of establishing the desired result in specific cases, we describe the properties of two well-known types of operators, namely the compact operators and quasitriangular operators. Finally, we show that if A is an algebra of compact operators or of triangular operators then A is similar to a <em>C</em>* algebra if and only if it has the total reduction property.

Description

Keywords

Mathematics, amenable, total reduction, invariant subspaces, similarity problems

LC Keywords

Citation

URI

http://hdl.handle.net/10012/2932

Collections

Theses
Pure Mathematics