Diagonals in Tensor Products of Operator Algebras

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dc.creatorPaulsen, Vern
dc.creatorSmith, Roger
dc.date2001-07-10
dc.date.accessioned2026-07-07T04:42:33Z
dc.date.available2026-07-07T04:42:33Z
dc.descriptionIn 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.
dc.description10 pages, latex file
dc.identifierhttps://arxiv.org/abs/math/0107077
dc.identifierhttp://arxiv.org/abs/math/0107077
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61829
dc.subjectOperator Algebras
dc.subject47L30
dc.titleDiagonals in Tensor Products of Operator Algebras
dc.typetext

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