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The free Banach lattice generated by a Banach space. (English) Zbl 1400.46015
Summary: 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 [Proc. R. Soc. Edinb., Sect. A, Math. 145, No. 1, 105–143 (2015; Zbl 1325.46020)]. 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.

MSC:
46B42 Banach lattices
46B50 Compactness in Banach (or normed) spaces
Citations:
Zbl 1325.46020
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References:
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