On certain classes of Markushevich bases
It is shown in this paper that if \(X\) is a Banach space for which \(X^*\) has a Markushevich basis \((u_ i,z_ i)\) with \([z_ i]\) containing \(X\) and \(B(X^*)\) is of countable tightness in the \(\omega^*\)-topology (see the paper for the technical definition), then \(X\) is weakly compactly generated. Other results (having similarly technical assumptions) which imply the non-existence of certain types of Markushevich bases are also derived.
scientific article; zbMATH DE number 590075
scientific article