On Spectral Properties of Orthogonal Isometries

Abstract

Isometries are special mappings with a property of distance preservation. This property makes them unique and interesting in-terms of characterization. However, it is very difficult to do characterizations of properties of isometires in a general Banach space setting due to the intricate underlying structures in Banach spaces. In this paper, we characterize spectral properties of isometries and in particular when they are orthogonal. We show that orthogonal isometries preserve distance even when they are subjected to direct sum decomposition.