Date of Award

Winter 1993

Project Type


Program or Major


Degree Name

Doctor of Philosophy

First Advisor

Donald Hadwin


In this paper we investigate approximate equivalence in von Neumann algebras. We find a necessary and sufficient condition for two normal operators to be approximately equivalent in any von Neumann algebra ${\cal R}$ acting on a separable Hilbert space H with unitaries in ${\cal R}.$ For the approximate equivalence of two unital representations from a given C$\*$-algebra to any von Neumann algebra acting on a separable Hilbert space, we find the necessary condition for the general case. Finally we investigate an interesting class of C$\*$-algebras, closed under direct sum, direct limit and quotient map, which contains C(X) and $M\sb{n}(A),$ where A is in Q.