A reflexivity criterion for Hilbert C*-modules over commutative C*-algebras

2009/08/10 by Michael Frank, M. Frank, Vladimir Manuilov +6
Mathematics · #46L08 #54D99 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #General Topology (math.GN) #Operator Algebras (math.OA) #math.GN #math.OA #msc:46L08 #msc:54D99

paper · pdf · doi:10.48550/arxiv.0908.1414

9 pages

openalex publication_date 2009/08/10 · arxiv created 2010/01/07 · arxiv updated 2010/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A C*-algebra A is C*-reflexive if any countably generated Hilbert C*-module M over A is C*-reflexive, i.e. the second dual module M'' coincides with M. We show that a commutative C*-algebra A is C*-reflexive if and only if for any sequence I_k of disjoint non-zero C*-subalgebras, the canonical inclusion ⊕_k I_k⊂ A doesn't extend to an inclusion of ∏_k I_k.

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