Duality and Operator Algebras II: Operator Algebras as Banach Algebras

Details Duality and Operator Algebras II: Operator Algebras as Banach Algebras Duality and Operator Algebras II: Operator Algebras as Banach Algebras

2004-08-20

arxiv.org/abs/math/0408281v2

Mathematics

Operator Algebras

To appear in J.F.A. Some minor corrections made

Scientific paper

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.

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