The free Banach lattice generated by a Banach space

2017/06/25 by Avilés, Antonio, Rodríguez, José, Tradacete, Pedro · 6 citations
#46B42 #46B50 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1706.08147

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.

Cited by

• Bourgain-uo sequential completeness in vector lattices
• Free quasi-Banach lattices
• Compact positive multilinear operators on Banach lattices
• Order denseness in free Banach lattices
• A universal approximation theorem and its applications to vector lattice theory
• Complemented subspaces of Banach lattices

Related

• The strong Nakano property in Banach lattices
• Free objects in Banach space theory
• Free dual spaces and free Banach lattices
• Free Banach lattices under convexity conditions
• Free Banach lattices generated by a lattice and projectivity