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m ‐isometries on Banach spaces
Author(s) -
Bayart Frédéric
Publication year - 2011
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200910029
Subject(s) - mathematics , isometry (riemannian geometry) , banach space , pure mathematics , hilbert space , focus (optics) , banach manifold , space (punctuation) , infinite dimensional vector function , lp space , computer science , physics , optics , operating system
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.