The M-basis Problem for Separable Banach Spaces

Abstract: In this note we show that, if $\mcB$ is separable Banach space, then there is a biorthogonal system ${x_n, x_n^*}$ such that, the closed linear span of ${x_n},\bar{\left\langle {{x_n}}\right\rangle}=\mcB$ and $\left| {x_n} \right|\left| {x_n^*} \right| = 1$ for all $n$.