On the relations between Auerbach or almost Auerbach Markushevich systems and Schauder bases (Q6592085)

W. B. Johnson proved that every separable Banach space contains an M-basis that is not a Schauder basis under any permutation [\textit{W.~B. Johnson}, Trans. Am. Math. Soc. 149, 171--177 (1970; Zbl 0194.43403)]. In the present paper, the authors study conditions on almost Auerbach M-bases to be Schauder bases and provide several constructions of almost Auerbach and Auerbach bases in separable Banach spaces that, under any permutation, are not equivalent to a Schauder basis.