On continuity of operators of metrical projection

Abstract

We consider the metric-projection operators in the space L^p(λ), 1 < p < ∞, where λ ∈ M^b, M^b being the space of bounded Randon measures. The metric-projection operators project a fixed element g ∈ C^b in L^p(λ) onto a closed convex subset K ⸦ C_u^b, where C_u^b is the space of bounded continuous functions in the topology of uniform convergence. We obtain statements on the continuity of the metric-projection operators, considered as mappings from M^b into K.