\(m\)-isometries on Banach spaces. (English) Zbl 1230.47018

Summary: We introduce the notion of an \(m\)-isometry of a Banach space, following a definition of J. Agler and M. Stankus [Integral Equations Oper. Theory 21, No. 4, 383–429 (1995; Zbl 0836.47008)] 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.


47A16 Cyclic vectors, hypercyclic and chaotic operators


Zbl 0836.47008
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