A few properties of the Kobayashi distance and their applications

Abstract

Let $N$ be a norming set in a Banach space $X$. In this paper we prove the lower semicontinuity with respect to the topology $\sigma( X,N)$ of the Kobayashi distance in a bounded, relatively compact in $\sigma ( X,N) $, convex and open subset of a Banach space. We apply this result to the Denjoy-Wolff type theorem.