SMOOTHLY EMBEDDED SUBSPACES OF A BANACH SPACE

Abstract

We say that a Banach space $Y$ embeds into a Banach space $X$ smoothly if there is a linear isometry $T$ from $Y$ into $X$ such that every subspace of $TY$ is Hahn-Banach smooth in $X$ (i.e., the ones with unique extension property). In this note, we show that they are exactly (isometric copies of) those subspaces of $X$ having the half-space property.