English

On projective Banach lattices of the form C(K) and FBL[E]

Functional Analysis 2020-04-13 v2

Abstract

We show that if a Banach lattice is projective, then every bounded sequence that can be mapped by a homomorphism onto the basis of c0c_0 must contain an 1\ell_1-subsequence. As a consequence, if Banach lattices p\ell_p or FBL[E]FBL[E] are projective, then p=1p=1 or EE has the Schur property, respectively. On the other hand, we show that C(K)C(K) is projective whenever KK is an absolute neighbourhood retract, answering a question by de Pagter and Wickstead.

Keywords

Cite

@article{arxiv.2002.12423,
  title  = {On projective Banach lattices of the form C(K) and FBL[E]},
  author = {Antonio Avilés and Gonzalo Martínez-Cervantes and José David Rodríguez Abellán},
  journal= {arXiv preprint arXiv:2002.12423},
  year   = {2020}
}