EXTREME AND SMOOTH POINTS INLORENTZ AND MARCINKIEWICZ SPACES WITHAPPLICATIONS TO CONTRACTIVE PROJECTIONS

摘要

We characterize extreme and smooth pointsin the Lorentz sequence space d(ω, 1) and in Marcinkiewiczsequence spaces d_*(ω, 1) and d~*(ω,1), which are predual anddual spaces to d(ω, 1), respectively. We then apply thesecharacterizations for studying the relationship between theexistence sets and one-complemented subspaces in d(ω, 1). Weshow that a subspace of d(ω, 1) is an existence set if and onlyif it is one-complemented.