IDEALS IN OPERATOR SPACE PROJECTIVE TENSOR PRODUCT OF C*-ALGEBRAS

Abstract

AbstractLet A and B be C*-algebras. We prove the slice map conjecture for ideals in the operator space projective tensor product $A \mathbin {\widehat {\otimes }} B$. As an application, a characterization of the prime ideals in the Banach *-algebra $A\mathbin {\widehat {\otimes }} B$ is obtained. In addition, we study the primitive ideals, modular ideals and the maximal modular ideals of $A\mathbin {\widehat {\otimes }} B$. We also show that the Banach *-algebra $A\mathbin {\widehat {\otimes }} B$ possesses the Wiener property and that, for a subhomogeneous C*-algebra A, the Banach * -algebra $A \mathbin {\widehat {\otimes }} B$ is symmetric.