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m‐isometries on Banach spaces

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.