Norming Markushevich bases: recent results and open problems

Abstract: We survey several results concerning norming Markushevich bases (M-bases, for short), focusing in particular on two recent examples of a weakly compactly generated Banach space with no norming M-basis and of an Asplund space with norming M-basis that is not weakly compactly generated. We highlight the context for these problems and state several open problems in different directions that arise from these results.