On the structure of multiplier algebras

Abstract

This note gives a characterization of matrix structures for multipliers of a stable $C^*$-algebra $A\otimes \mathcal{K} $ with any $C^*$-algebra $A$. We represent elements in $(A\otimes \mathcal{K} )''$, $QM(A\otimes \mathcal{K} )$ and $M(A\otimes \mathcal{K} )$ as infinite matrices over certain $C^*$-algebras, respectively. These results generalize the related work of Brown, Lin and Zhang in this area.