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Journal of Function Spaces and Applications
Volume 2013, Article ID 782792, 8 pages
Research Article

The Köthe Dual of an Abstract Banach Lattice

1Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, Campus Fuentenueva S/N, 18071 Granada, Spain
2Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera S/N, 46022 Valencia, Spain

Received 28 May 2013; Accepted 6 June 2013

Academic Editor: Miguel Martin

Copyright © 2013 E. Jiménez Fernández et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We analyze a suitable definition of Köthe dual for spaces of integrable functions with respect to vector measures defined on δ-rings. This family represents a broad class of Banach lattices, and nowadays it seems to be the biggest class of spaces supported by integral structures, that is, the largest class in which an integral representation of some elements of the dual makes sense. In order to check the appropriateness of our definition, we analyze how far the coincidence of the Köthe dual with the topological dual is preserved.