Extensions of linear operators from hyperplanes and strong uniqueness of best approximation in [formula omitted

Abstract

The aim of this paper is to present some results concerning the problem of minimal projections and extensions. Let X be a reflexive Banach space and let Y be a closed subspace of X of codimension one. Let W be a finite-dimensional Banach space. We present a new sufficient condition under which any minimal extension of an operator A∈L(Y,W) is strongly unique. In this paper we show (in some circumstances) that if 1<λ(Y,X), then a minimal projection from X onto Y is a strongly unique minimal projection. Moreover, we introduce and study a new geometric property of normed spaces. In this paper we also present a result concerning the strong unicity of best approximation.