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DIAGONALS IN TENSOR PRODUCTS OF OPERATOR ALGEBRAS
Published online by Cambridge University Press: 14 October 2002
Abstract
In this paper we give a short, direct proof, using only properties of the Haagerup tensor product, that if an operator algebra $A$ possesses a diagonal in the Haagerup tensor product of $A$ with itself, then $A$ must be isomorphic to a finite-dimensional $C^*$-algebra. Consequently, for operator algebras, the first Hochschild cohomology group $H^1(A,X)=0$ for every bounded, Banach $A$-bimodule $X$, if and only if $A$ is isomorphic to a finite-dimensional $C^*$-algebra.
AMS 2000 Mathematics subject classification: Primary 46L06. Secondary 46L05
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 3 , October 2002 , pp. 647 - 652
- Copyright
- Copyright © Edinburgh Mathematical Society 2002
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