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arXiv · 1408.0040

Weak Sequential Completeness in Banach $C(K)$-modules of finite multiplicity

Arkady Kitover·Mehmet Orhon
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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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BibTeXRIS

Arkady Kitover, Mehmet Orhon. 2014-07-31. Weak Sequential Completeness in Banach $C(K)$-modules of finite multiplicity. https://arxiv.org/abs/1408.0040

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