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arXiv · 1106.3143

Ideals in Operator Space Projective Tensor Product of $C^*$-algebras

Ranjana Jain·Ajay Kumar
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Abstract

For $C^*$-algebras $A$ and $B$, we prove the slice map conjecture for ideals in the operator space projective tensor product $A \hat\otimes B$. As an application, a characterization of prime ideals in the Banach $\ast$-algebra $A\hat\otimes B$ is obtained. Further, we study the primitive ideals, modular ideals and the maximal modular ideals of $A\hat\otimes B$. It is also shown that the Banach $\ast$-algebra $A\hat\otimes B$ possesses Wiener property; and that, for a subhomogenous $C^*$-algebra $A$, $A\hat\otimes B$ is symmetric.

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Ranjana Jain, Ajay Kumar. 2011-06-16. Ideals in Operator Space Projective Tensor Product of $C^*$-algebras. https://arxiv.org/abs/1106.3143

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