Two new examples of Banach spaces with a plastic unit ball

Abstract

We prove that Banach spaces ${\ell }_1{\oplus }_2\mathbb{R}$ and $X{\oplus }_{\infty }Y$, with strictly convex $X$ and $Y$, have plastic unit balls (we call a metric space plastic if every non-expansive bijection from this space onto itself is an isometry).