Positivity

, Volume 18, Issue 3, pp 475–488 | Cite as

Reflexivity of Banach \(C(K)\)-modules via the reflexivity of Banach lattices

Article

Abstract

We extend the well known criteria of reflexivity of Banach lattices due to Lozanovsky and Lotz to the class of finitely generated Banach \(C(K)\)-modules. Namely we prove that a finitely generated Banach \(C(K)\)-module is reflexive if and only if it does not contain any subspace isomorphic to either \(l^{1}\) or \(c_{0}\).

Keywords

Reflexivity Banach \(C(K)\)-modules Banach lattices 

Mathematics Subject Classification (1991)

Primary 46B10 46A25 Secondary 46B42 

Notes

Acknowledgments

We are grateful to H. Rosenthal and T. Oikhberg, respectively, for remarks that allowed us to simplify condition (3) of Theorem 1 and the proof of Lemma 3, respectively.

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of MathematicsCommunity College of PhiladelphiaPhiladelphiaUSA
  2. 2.Department of Mathematics and StatisticsUniversity of New HampshireDurhamUSA

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