Simultaneous projectional skeletons

TL;DR

This paper proves the existence of simultaneous projectional skeletons in certain subspaces of continuous function spaces, generalizing previous results and providing new characterizations of Asplund spaces.

Contribution

It introduces a new existence theorem for simultaneous projectional skeletons in specific subspaces of C(K) spaces, extending Valdivia's work.

Findings

Provides a new characterization of Asplund spaces.

Generalizes previous results on projectional resolutions of identity.

Collects consequences of the main theorem.

Abstract

We prove the existence of a simultaneous projectional skeleton for certain subspaces of $\mathcal{C}(K)$ spaces. This generalizes a result on simultaneous projectional resolutions of identity proved by M. Valdivia. We collect some consequences of this result. In particular we give a new characterization of Asplund spaces using the notion of projectional skeleton.