International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 65-68, Pages 3663-3670
doi:10.1155/S0161171204401057
Proximinality in generalized direct sums
Darapaneni Narayana1
and T.S.S.R.K. Rao2
1Equipe d'Analyse, Université Paris 6, 4 Place Jussieu, Paris Cedex 05 75252, France
2Statistics and Mathematics Unit, Indian Statistical Institute, Bangalore 560059, India
Abstract
We consider proximinality and transitivity of proximinality for subspaces of finite codimension in generalized direct sums of Banach spaces. We give several examples of Banach spaces where proximinality is transitive among subspaces of finite codimension.