The free Banach lattice generated by a Banach space. Articles uri icon

authors

  • AVILÉS, ANTONIO
  • RODRÍGUEZ, JOSÉ
  • TRADACETE PEREZ, PEDRO

publication date

  • May 2018

start page

  • 2995

end page

  • 2977

issue

  • 10

volume

  • 274

International Standard Serial Number (ISSN)

  • 0022-1236

Electronic International Standard Serial Number (EISSN)

  • 1096-0783

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. (C) 2018 Elsevier Inc. All rights reserved.

keywords

  • banach lattice; free lattice; nakano property; weakly compactly generated space.