Minimal projections and absolute projection constants for regular polyhedral spaces

Abstract:

Let $V = [{v_1}, \ldots ,{v_n}]$ be the $n$-dimensional space of coordinate functions on a set of points $\tilde v \subset {{\mathbf {R}}^n}$ where $\tilde v$ is the set of vertices of a regular convex polyhedron. In this paper the absolute projection constant of any $n$-dimensional Banach space $E$ isometrically isomorphic to $V \subset C(\tilde v)$ is computed, examples of which are the well-known cases $E = l_n^\infty ,l_n^1$.