Abstract and Applied Analysis
Volume 2009 (2009), Article ID 562507, 8 pages
doi:10.1155/2009/562507
Research Article

Some Properties of lp(A,X) Spaces

Xiaohong Fu and Songxiao Li

Department of Mathematics, JiaYing University, Meizhou, GuangDong 514015, China

Received 27 January 2009; Revised 26 March 2009; Accepted 21 April 2009

Academic Editor: Stevo Stevic

Copyright © 2009 Xiaohong Fu and Songxiao Li. 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 provide a representation of elements of the space lp(A,X) for a locally convex space X and 1≤p<∞ and determine its continuous dual for normed space X and 1<p<∞. In particular, we study the extension and characterization of isometries on lp(N,X) space, when X is a normed space with an unconditional basis and with a symmetric norm. In addition, we give a simple proof of the main result of G. Ding (2002).