Some Properties of lp(A,X) Spaces

Abstract

We provide a representation of elements of the space $l^p\left(A,X\right)$ for a locally convex space $X$ and $1\le p<\infty$ and determine its continuous dual for normed space $X$ and $1<p<\infty$. In particular, we study the extension and characterization of isometries on $l^p\left(\text{N},X\right)$ 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).