NONEXPANSIVE METRIC PROJECTIONS IN SPACES OF CONTINUOUS FUNCTIONS

YOAV BENYAMINI

Abstract. Let K be a subset of a Banach space E. We discuss the existence of a retraction φ : E → K which is simultaneously nonexpansive and a nearest point map. (We shall then say that K is a proximinal nonexpansive retract of E.)

Among other results we characterize subspaces of codimension one in spaces C(S) of continuous functions which are proximinal nonexpansive retracts of C(S) as well as the proximinal nonexpansive retracts in l_{∞}^{n}.

This is joint work with Rafael Espínola and Genaro López.