International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 7, Pages 383-392
doi:10.1155/S0161171202012772

On β-dual of vector-valued sequence spaces of Maddox

Suthep Suantai and Winate Sanhan

Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Abstract

The β-dual of a vector-valued sequence space is defined and studied. We show that if an X-valued sequence space E is a BK-space having AK property, then the dual space of E and its β-dual are isometrically isomorphic. We also give characterizations of β-dual of vector-valued sequence spaces of Maddox ℓ(X,p), ℓ∞(X,p), c0(X,p), and c(X,p).