Simultaneous projectional skeletons

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.

References in corpus (2)

• Banach spaces with projectional skeletons
• Compactness in Banach space theory - selected problems

Cited by in corpus (4)

• Monotone retractability and retractional skeletons
• On Markushevich bases in preduals of von Neumann algebras
• Projectional skeletons and Markushevich bases
• Characterization of compact monotonically ($\omega$)-monolithic spaces using system of retractions