A fixed point theorem for isometries on a metric space
Andrzej Wiśnicki- Applied Mathematics
- General Mathematics
Abstract
We show that if X is a complete metric space with uniform relative normal
structure and G is a subgroup of the isometry group of X with bounded
orbits, then there is a point in X fixed by every isometry in G. As a
corollary, we obtain a theorem of U. Lang (2013) concerning injective metric
spaces. A few applications of this theorem are given to the problems of
inner derivations. In particular, we show that if