On projection constant problems and the existence of metric projections in normed spaces

摘要

We give the sufficient conditions for the existence of a metricprojection onto convex closed subsets of normed linear spaceswhich are reduced conditions than that in the case of reflexiveBanach spaces and we find a general formula for the projectionsonto the maximal proper subspaces of the classical Banach spacesl?p,1≤p<∞andc?0. We also give the sufficientand necessary conditions for an infinite matrix to represent aprojection operator froml?p,1≤p<∞orc?0ontoanyone of their maximal proper subspaces.