On the three-spaces problem and extension of MLUR norms on Banach spaces

Abstract

We show that if $X$ is a Banach space, $Y$ is a subspace of $X$ which admits an equivalent midpoint locally uniformly rotund (MLUR) norm $||.||$ and if $X/Y$ is separable, then the norm $||.||$ has an extension which is a MLUR norm on $X$