About this Journal Submit a Manuscript Table of Contents
Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 902694, 9 pages
http://dx.doi.org/10.1155/2013/902694
Research Article

Intersection Properties of Balls in Banach Spaces

Stat-Math Unit, Indian Statistical Institute, R. V. College Post, Bangalore 560059, India

Received 29 May 2013; Revised 25 July 2013; Accepted 20 August 2013

Academic Editor: Miguel Martin

Copyright © 2013 C. R. Jayanarayanan. 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 introduce a weaker notion of central subspace called almost central subspace, and we study Banach spaces that belong to the class (GC), introduced by Veselý (1997). In particular, we prove that if is an almost central subspace of a Banach space such that is in the class (GC), then is a central subspace of . We also prove that if  is a semi -ideal in a Banach space such that is an almost central subspace of , then is an -ideal in . Certain stability results for quotient spaces, injective tensor product spaces, and polyhedral direct sums of Banach spaces are also derived.