On projectional skeletons in Va\v{s}\'ak spaces

TL;DR

This paper offers a new, simpler proof that all Vašák spaces have a full 1-projectional skeleton, using elementary submodels, extending known results to a broader class of Banach spaces.

Contribution

It provides an alternative, elementary proof of the existence of 1-projectional skeletons in Vašák spaces, simplifying previous methods.

Findings

Vašák spaces admit full 1-projectional skeletons

The proof uses elementary submodels for simplicity

Extends known results to weakly countably determined spaces

Abstract

We provide an alternative proof of the theorem saying that any Va\v{s}\'ak (or, weakly countably determined) Banach space admits a full $1$-projectional skeleton. The proof is done with the use of the method of elementary submodels and is comparably simple as the proof given by W.~Kubi\'s (2009) in case of weakly compactly generated spaces.