The Representations and Continuity of the Metric Projections on Two Classes of Half-Spaces in Banach Spaces

Abstract EN

We show a necessary and sufficient condition for the existence of metric projection on a class of half-space Kx0*,c={x∈X:x*(x)≤c} in Banach space.

Two representations of metric projections PKx0*,c and PKx0,c are given, respectively, where Kx0,c stands for dual half-space of Kx0*,c in dual space X*.

By these representations, a series of continuity results of the metric projections PKx0*,c and PKx0,c are given.

We also provide the characterization that a metric projection is a linear bounded operator.