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

Abstract

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 l n ∞ (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 l k+m−1 ∞ . As such the aforementioned estimation can be applied to spaces other than l n ∞ . We also include a conjecture about the exact calculations of SUP-constants in particular settings.

A note on generalized projections in c0

“…For results concerning strong uniqueness in general and in the context of minimal projections see e.g. [1], [2], [18], [19], [23], [24], [26], [28], [32].…”