<i>m</i>‐isometries on Banach spaces

Abstract

Abstract We introduce the notion of an m ‐isometry of a Banach space, following a definition of Agler and Stankus in the Hilbert space setting. We give a first approach to the general theory of these maps. Then, we focus on the dynamics of m ‐isometries, showing that they are never N ‐supercyclic. This result is new even on a Hilbert space, and even for isometries on a general Banach space.