Date of Award
Winter 1993
Abstract
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.
Document Type
Dissertation
First Advisor
Donald Hadwin
Department or Program
Mathematics
Degree Name
Doctor of Philosophy
Recommended Citation
Ding, Hui-Ru, "Approximate equivalence invon Neumann algebras" (1993). Doctoral Dissertations. 1764.
https://scholars.unh.edu/dissertation/1764