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Duality and Operator Algebras II: Operator Algebras as Banach Algebras

2004/08/20 by David P. Blecher, Blecher, David P., Bojan Magajna +1
Mathematics · #46L07 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:46L07

paper · pdf · doi:10.48550/arxiv.math/0408281

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

openalex publication_date 2004/08/20 · arxiv created 2004/12/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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