Symmetry and quasi-centrality of operator space projective tensor product

Abstract

For $C^{\ast }$-algebras $A$ and $B$, the operator space projective tensor product $A\hat{\otimes }B$ and the Banach space projective tensor product $A{\otimes }_{\gamma }B$ are shown to be symmetric. We also show that $A\hat{\otimes }B$ is weakly Wiener algebra. Finally, quasi-centrality, and the unitary group of $A\hat{\otimes }B$ are discussed.