Nonunital multiplier pairs and remarks on generalized group C*-algebras

<p>In the first part of this paper we will consider a generalization of D. Hadwin and E. Nordgren's work on multiplier pairs. Here we will not assume the existence of an identity, but rather just ask for the existence of a bounded approximate identity. Without the assumption of the identity, we find a new result concerning the relationship between the norm closure of the left multiplication operators and the approximate double commutant of the left multiplication operators.</p><p>In the second part we will suppose f, g : T&amp;rarr;T are continuous functions on the unit circle T and let B (f, g) denote the universal C*-algebra generated by U and V subject to the conditions that U and V are a unitary, and Uf( V)U-1 = g( V). We then will prove that this C*-algebra may be represented as a crossed product. Next we will show that under certain conditions on f or g, B (f, g) will be nuclear, weakly quasidiagonal and we will be able to compute its Ext group. In the last two sections we will give a partial description of the K1-group of B (f, g) and then using the results from [DH] calculate the free entropy dimension of B (f, g).</p><p>In the third and last part of this paper we show that the standard family of independent unitary n x n random matrices remains an asymptotically free Haar unitary with respect to any state 4:Mn C &amp;rarr;C . The result was originally stated by Voiculescu for the normalized trace. Our work here will follow the modified version of Voiculescu's theorem given by D. Hadwin and M. Dostal in [DH].</p>

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Dissertation

Year

2005

Author dc:creator

• Zak, Sandra E

Contributors dc:contributor

• Donald Hadwin

• Mathematics

Repository record dc:identifier

https://scholars.unh.edu/dissertation/295

OAI identifier oai:identifier

oai:scholars.unh.edu:dissertation-1294