Abelian strict approximation in $AW^*$-algebras and Weyl-von Neumann type theorems
Abelian strict approximation in $AW^*$-algebras and Weyl-von Neumann type theorems
In this paper, for a $C^*$-algebra $A$ with $M=M(A)$ an $AW^*$-algebra, or equivalently, for an essential, norm-closed, two-sided ideal $A$ of an $AW^*$-algebra $M$, we investigate the strict approximability of the elements of $M$ from commutative $C^*$-subalgebras of $A$. In the relevant case of the norm-closed linear span $A$ of …