International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 67, Pages 3663-3670

Proximinality in generalized direct sums

Darapaneni Narayana1,2 and T. S. S. R. K. Rao3

1Equipe d'Analyse, Université Paris 6, 4 Place Jussieu, Paris Cedex 05 75252, France
2Department of Mathematics, Indian Institute of Sciences, Bangalore 560012, India
3Statistics and Mathematics Unit, Indian Statistical Institute, Bangalore 560059, India

Received 8 January 2004

Copyright © 2004 Darapaneni Narayana and T. S. S. R. K. Rao. 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.


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.