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Currently I'm reading the paper by Abadie and Ferraro titled Applications of ternary rings to $C^*$-algebras. Recall that a $C^{\ast}$-ternary ring is a complex Banach space $M$, equipped with a ...

Let $A$ and $B$ be $C^{\ast}$-algebras. It is well known that maximal tensor product of simple $C^{\ast}$-algebras need not be simple. So basically the ideal structure of $A\otimes_{max}B$ does not ...

This is a crosspost from math.se because it did not get any attention whatsoever. I therefore assume that it fits here better. Let $\mathcal{A}$ be a $C^*$-algebra and $A \in \mathcal{A}$. I am ...