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

Antonio Avilés; Gonzalo Martínez-Cervantes; José David Rodríguez Abellán

doi:10.1016/j.jmaa.2020.124129

paper

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

arXiv:2002.12423 · doi:10.1016/j.jmaa.2020.124129

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 $c_{0}$ must contain an $ℓ_{1}$ -subsequence. As a consequence, if Banach lattices $ℓ_{p}$ or $F B L [E]$ are projective, then $p = 1$ or $E$ has the Schur property, respectively. On the other hand, we show that $C (K)$ is projective whenever $K$ is an absolute neighbourhood retract, answering a question by de Pagter and Wickstead.