English

On the c_0-extension property

Functional Analysis 2020-05-26 v2

Abstract

In this work we investigate the c_0-extension property. This property generalizes Sobczyk's theorem in the context of nonseparable Banach spaces. We prove that a sufficient condition for a Banach space to have this property is that its closed dual unit ball is weak-star monolithic. We also present several results about the c_0-extension property in the context of C(K) Banach spaces. An interesting result in the realm of C(K) spaces is that the existence of a Corson compactum K such that C(K) does not have the c_0-extension property is independent from the axioms of ZFC.

Keywords

Cite

@article{arxiv.1912.08564,
  title  = {On the c_0-extension property},
  author = {Claudia Correa},
  journal= {arXiv preprint arXiv:1912.08564},
  year   = {2020}
}

Comments

Final version, accepted for publication in Studia Mathematica

R2 v1 2026-06-23T12:49:38.500Z