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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:489

Article

Aviles, Antonio¹  Martinez-Cervantes, Gonzalo¹  Rodriguez Abellan, Jose David¹ 

[1] Univ Murcia, Dept Matemat, Campus Espinardo, Murcia 30100, Spain

关键词: Schur property;    Banach space;    Banach lattice;    Free Banach lattice;    Projectivity;    FBL[E];   

DOI  :  10.1016/j.jmaa.2020.124129

来源: Elsevier

【 摘 要 】

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 FBL[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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free