Remark on a Paper of Sababheh and Khalil

Abstract

We show that any Banach space X that has a sequence of unit vectors weakly converging to 0 has a closed and bounded convex set that is not remotal. This extends the main result of Sababheh and Khalil, (Numer. Funct. Anal. Optim. 2008; 29:1166–1170).

Keywords:

• Reflexive Banach spaces
• Remotal sets

Mathematics Subject Classification 2000:

• Primary 46B20
• Secondary 41A50