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Bayart, Frédéric

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

Math. Nachr. 284, No. 17-18, 2141-2147 (2011).
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.

Cited in 2 Reviews
Cited in 31 Documents

MSC:

47A16 Cyclic vectors, hypercyclic and chaotic operators

Keywords:

supercyclic operators; \(m\)-isometry

Citations:

Zbl 0836.47008
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\textit{F. Bayart}, Math. Nachr. 284, No. 17--18, 2141--2147 (2011; Zbl 1230.47018)
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References:

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[2] Agler, m-isometric transformations of Hilbert space. II, Integral Equations Oper. Theory 23 pp 1– (1995) · Zbl 0857.47011
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