Local isometries of L(X, C(K))

Abstract

In this paper we study the structure of local isometries on LX, C(K)). We show that when K is first countable and X is uniformly convex and the group of isometries of X^∗ is algebraically reflexive, the range of a local isometry contains all compact operators. When X is also uniformly smooth and the group of isometries of X^∗ is algebraically reflexive, we show that a local isometry whose adjoint preserves extreme points is a C(K)-module map.