English

Projectional skeletons and Markushevich bases

Functional Analysis 2019-09-17 v3

Abstract

We prove that Banach spaces with a 11-projectional skeleton form a P\mathcal{P}-class and deduce that any such space admits a strong Markushevich basis. We provide several equivalent characterizations of spaces with a projectional skeleton and of spaces having a commutative one. We further analyze known examples of spaces with a non-commutative projectional skeleton and compare their behavior with the commutative case. Finally, we collect several open problems.

Keywords

Cite

@article{arxiv.1805.11901,
  title  = {Projectional skeletons and Markushevich bases},
  author = {Ondřej F. K. Kalenda},
  journal= {arXiv preprint arXiv:1805.11901},
  year   = {2019}
}

Comments

67 pages, references were updated, remark on solution of one questions was added, few minor changes were made

R2 v1 2026-06-23T02:13:07.406Z