The Representive of Metric Projection on the Finite Codimension Subspace in Banach Space

Abstract

In the paper we introduce the notions of the separation factor $κ$ and give a representive of metric projection on an $n$-codimension subspace (or an affine set) under certain conditions in Banach space. Further, we obtain the distance formula from any point $x$ to a finite $n$-codimension subspace. Results extend and improve the corresponding results in Hilbert space.