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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Authors: Ajay Kumar and 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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Additional Information

Ajay Kumar
Affiliation: Department of Mathematics, Rajdhani College (University of Delhi), Raja Garden, New Delhi-110015, India

Allan M. Sinclair
Affiliation: Department of Mathematics and Statistics, University of Edinburgh, James Clerk Maxwell Building, King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, Scotland
Email: allan@maths.ed.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02190-4
PII: S 0002-9947(98)02190-4
Keywords: Banach space projective norm, operator space projective norm, Haagerup norm, $C^*$-algebras, second dual
Received by editor(s): August 16, 1996
Additional Notes: Supported by Commonwealth Academic Staff Fellowship at the University of Edinburgh
Article copyright: © Copyright 1998 American Mathematical Society