A lower bound of the strongly unique minimal projection constant of , n⩾3

In this paper we give a lower bound for the strongly unique minimal projection (with norm one) constant (SUP-constant) onto some (n-k)-dimensional subspaces of (n⩾3, 1⩽k⩽n-1). By Proposition 1 of this paper, each k-dimensional Banach space with polytope unit ball with m (k-1)-dimensional faces is isometrically isomorphic to a subspace of . As such the aforementioned estimation can be applied to spaces other than . We also include a conjecture about the exact calculations of SUP-constants in particular settings.