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 $\{x_n,x_n^{\ast }\}$ such that, the closed linear span of $\{x_n\},\bar{\left\langle {\{x_n\}}\right\rangle}=\mcB$ and $\Vert x_n\Vert \Vert x_n^{\ast }\Vert =1$ for all $n$.