Abstract and Applied Analysis 
Volume 6 (2001), Issue 7, Pages 401-411
doi:10.1155/S1085337501000732

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

Entisarat El-Shobaky,1 Sahar Mohammed Ali,1 and Wataru Takahashi2

 1Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt
2Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan
Received 3 September 2001

Abstract

We give the sufficient conditions for the existence of a metric projection onto convex closed subsets of normed linear spaces which are reduced conditions than that in the case of reflexive Banach spaces and we find a general formula for the projections onto the maximal proper subspaces of the classical Banach spaces l p,1≤p<∞ and c 0. We also give the sufficient and necessary conditions for an infinite matrix to represent a projection operator from l p,1≤p<∞ or c 0 onto anyone of their maximal proper subspaces.