## $$m$$-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.

### MSC:

 47A16 Cyclic vectors, hypercyclic and chaotic operators

### Keywords:

supercyclic operators; $$m$$-isometry

Zbl 0836.47008
Full Text:

### References:

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