Some Properties of lp(A,X) Spaces

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)