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ISSN 1088-6850(e) ISSN 0002-9947(p)

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

Author(s): Ajay Kumar; Allan M. Sinclair
Journal: Trans. Amer. Math. Soc. 350 (1998), 2033-2048.
MSC (1991): Primary 46L05; Secondary 46C10, 47035
MathSciNet review: 1473449
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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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