Projectional skeletons and Markushevich bases

We prove that Banach spaces with a \(1\)-projectional skeleton form a \(\mathcal{P}\)-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.