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

Copyright © 2001 Entisarat El-Shobaky et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.