Nonseparable Approximate Equivalence
Nonseparable Approximate Equivalence
This paper extends Voiculescu’s theorem on approximate equivalence to the case of nonseparable representations of nonseparable ${C^ \ast }$-algebras. The main result states that two representations $f$ and $g$ are approximately equivalent if and only if ${\text {rank}}f(x) = {\text {rank}}g(x)$ for every $x$. For representations of separable ${C^ \ast …