Some Properties oflp(A,X)Spaces

Abstract

We provide a representation of elements of the spacelp(A,X)for a locally convex spaceXand1≤p<∞and determine its continuous dual for normed spaceXand1<p<∞. In particular, we study the extension and characterization of isometries onlp(N,X)space, whenXis 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).