1-Grothendieck $C(K)$ spaces
Functional Analysis
2015-11-09 v1
Abstract
A Banach space is said to be Grothendieck if weak and weak convergent sequences in the dual space coincide. This notion has been quantificated by H. Bendov\'{a}. She has proved that has the quantitative Grothendieck property, namely, it is 1-Grothendieck. Our aim is to show that Banach spaces from a certain wider class are 1-Grothendieck, precisely, is 1-Grothendieck provided is a totally disconnected compact space such that its algebra of clopen subsets has the so called Subsequential completeness property.
Cite
@article{arxiv.1511.02202,
title = {1-Grothendieck $C(K)$ spaces},
author = {Jindřich Lechner},
journal= {arXiv preprint arXiv:1511.02202},
year = {2015}
}