2009/02/24 by M. Frank, Michael Frank, Frank, M. +3
Computer Science · Decision Sciences · Mathematics · #46L08 #Advanced Algebra and Logic #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Multi-Criteria Decision Making #Operator Algebras (math.OA) #math.FA #math.OA #msc:46L08
paper · pdf · doi:10.48550/arxiv.0902.4107
19 pages / replaced with minor additions, corrections, reformulations
openalex publication_date 2009/02/24 · arxiv created 2009/10/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Continuing the research on the Banach-Saks and Schur properties started in (cf. M. Frank, A. A. Pavlov, Banach-Saks properties of C*-algebras and Hilbert C*-modules (submitted)) we investigate analogous properties in the module context. As an environment serves the class of Hilbert C*-modules. Some properties of weak module topologies on Hilbert C*-modules are described. Natural module analogues of the classical weak Banach-Saks and the classical Schur properties are defined and studied. A number of useful characterizations of properties of Hilbert C*-modules is obtained. In particular, some interrelations of these properties with the self-duality property of countably generated Hilbert C*-modules are established.