Duality and Operator Algebras II: Operator Algebras as Banach Algebras

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We answer, by counterexample, several open questions concerning algebras of operators on a Hilbert space. The answers add further weight to the thesis that, for many purposes, such algebras ought to be studied in the framework of operator spaces, as opposed to that of Banach spaces and Banach algebras. In particular, the `nonselfadjoint analogue' of a W*-algebra resides naturally in the category of dual operator spaces, as opposed to dual Banach spaces. We also show that an automatic w*-continuity result in the preceding paper of the authors is sharp.
To appear in J.F.A. Some minor corrections made

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Operator Algebras, Functional Analysis, 46L07

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http://salesiana.dossiersoluciones.com/handle/123456789/72241

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0408281
 http://arxiv.org/abs/math/0408281

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arXiv