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arXiv · 1805.11901

Projectional skeletons and Markushevich bases

Ondřej F. K. Kalenda
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Abstract

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.

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Ondřej F. K. Kalenda. 2018-05-30. Projectional skeletons and Markushevich bases. https://doi.org/10.1112/plms.12299

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