Abstract
We prove that Banach spaces with a 1-projectional skeleton form a 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 noncommutative projectional skeleton and compare their behavior with the commutative case. Finally, we collect several open problems.
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