On the $c_0$-extension property
Volume 256 / 2021
Studia Mathematica 256 (2021), 345-359
MSC: Primary 46B26, 46E15; Secondary 03E35, 54G12.
DOI: 10.4064/sm191218-24-5
Published online: 4 August 2020
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 of the axioms of ZFC.
