Equivalence of norms on operator space tensor products of 𝐶*-algebras

Kumar, Ajay; Sinclair, Allan

doi:10.1090/S0002-9947-98-02190-4

Equivalence of norms on operator space tensor products of $C^\ast$-algebras
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by Ajay Kumar and Allan M. Sinclair PDF

Trans. Amer. Math. Soc. 350 (1998), 2033-2048 Request permission

Abstract:

The Haagerup norm $\Vert \cdot \Vert _{h}$ on the tensor product $A\otimes B$ of two $C^*$-algebras $A$ and $B$ is shown to be Banach space equivalent to either the Banach space projective norm $\Vert \cdot \Vert _{\gamma }$ or the operator space projective norm $\Vert \cdot \Vert _{\wedge }$ if and only if either $A$ or $B$ is finite dimensional or $A$ and $B$ are infinite dimensional and subhomogeneous. The Banach space projective norm and the operator space projective norm are equivalent on $A\otimes B$ if and only if $A$ or $B$ is subhomogeneous.

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