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