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

Weak sequential completeness in Banach $$C(K)$$ 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 $$c_{0}$$ c 0 . In the current paper we extend this result to the class of Banach $$C(K)$$ C ( K ) -modules of finite multiplicity and, as a special case, to finitely generated Banach $$C(K)$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

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

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Publisher
Springer International Publishing
Copyright
Copyright © 2015 by Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-015-0340-x
Publisher site
See Article on Publisher Site

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 $$c_{0}$$ c 0 . In the current paper we extend this result to the class of Banach $$C(K)$$ C ( K ) -modules of finite multiplicity and, as a special case, to finitely generated Banach $$C(K)$$ 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.

Journal

PositivitySpringer Journals

Published: May 23, 2015

References

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