On projection constant problems and the existence of metric projections in normed spaces

Abstract

We give the sufficient conditions for the existence of a metric projection onto convex closed subsets of normed linear spaces which are reduced conditions than that in the case of reflexive Banach spaces and we find a general formula for the projections onto the maximal proper subspaces of the classical Banach spaces and $c_0$. We also give the sufficient and necessary conditions for an infinite matrix to represent a projection operator from or $c_0$ onto anyone of their maximal proper subspaces.