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
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Received 13 April 2001; Revised 10 October 2001
Copyright © 2002 Suthep Suantai and Winate Sanhan. 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
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).