The free Banach lattices generated by lp and c0 Articles uri icon

authors

  • AVILÉS, ANTONIO
  • TRADACETE PEREZ, PEDRO
  • VILLANUEVA, IGNACIO

publication date

  • May 2019

start page

  • 353

end page

  • 364

issue

  • 2

volume

  • 32

International Standard Serial Number (ISSN)

  • 1139-1138

Electronic International Standard Serial Number (EISSN)

  • 1988-2807

abstract

  • We prove that, when 2 < p < ∞, in the free Banach lattice generated by p (respectively by c0), the absolute values of the canonical basis form an r-sequence, where [...] (respectively an l2-sequence). In particular, in any Banach lattice, the absolute values of any p sequence always have an upper r-estimate. Quite surprisingly, this implies that the free Banach lattices generated by the nonseparable [...], are weakly compactly generated whereas this is not the case for 1 ≤ p ≤ 2.

subjects

  • Mathematics

keywords

  • banach lattice; free lattice; weakly compactly generated space