Weak sequential completeness in Banach $$C(K)$$ -modules of finite multiplicity.

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. [ABSTRACT FROM AUTHOR]