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The free Banach lattice generated by a Banach space

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 May 2018Embargo end date: 01 Jan 2017Publisher:Elsevier BVJournal:Journal of Functional Analysis, volume 274, pages 2,955-2,977 (issn: 0022-1236,

Authors: Pedro Tradacete; José Rodríguez; Antonio Avilés;

doi: 10.1016/j.jfa.2018.03.001 , 10.48550/arxiv.1706.08147

arXiv: http://arxiv.org/abs/1706.08147

The free Banach lattice generated by a Banach space

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Abstract

The free Banach lattice over a Banach space is introduced and analyzed. This generalizes the concept of free Banach lattice over a set of generators, and allows us to study the Nakano property and the density character of non-degenerate intervals on these spaces, answering some recent questions of B. de Pagter and A.W. Wickstead. Moreover, an example of a Banach lattice which is weakly compactly generated as a lattice but not as a Banach space is exhibited, thus answering a question of J. Diestel.

Related Organizations

Carlos III University of Madrid
Spain
University of Murcia
Spain

Keywords

Mathematics - Functional Analysis, FOS: Mathematics, 46B42, 46B50, Functional Analysis (math.FA)

3 Research products, page 1 of 1

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