Abstract
A well known result of Lozanovsky states that a Banach lattice is weakly sequentially complete if and only if it does not contain a copy of \(c_{0}\). In the current paper we extend this result to the class of Banach \(C(K)\)-modules of finite multiplicity and, as a special case, to finitely generated Banach \(C(K)\)-modules. Moreover, we prove that such a module is weakly sequentially complete if and only if each cyclic subspace of the module is weakly sequentially complete.
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Notes
By subspace we always mean closed subspace.
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Kitover, A., Orhon, M. Weak sequential completeness in Banach \(C(K)\)-modules of finite multiplicity. Positivity 21, 739–753 (2017). https://doi.org/10.1007/s11117-015-0340-x
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DOI: https://doi.org/10.1007/s11117-015-0340-x