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arXiv · 1902.08492

Some examples of $m$-isometries

T. Bermúdez·A. Martinón·H. Zaway
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Abstract

We obtain the admissible sets on the unit circle to be the spectrum of a strict $m$-isometry on an $n$-finite dimensional Hilbert space. This property gives a better picture of the correct spectrum of an $m$-isometry. We determine that the only $m$-isometries on $\mathbb{R}^2$ are $3$-isometries and isometries giving by $\pm I+Q$, where $Q$ is a nilpotent operator. Moreover, on real Hilbert space, we obtain that $m$-isometries preserve volumes. Also we present a way to construct a strict $(m+1)$-isometry with an $m$-isometry given, using ideas of Aleman and Suciu \cite[Proposition 5.2]{AS} on infinite dimensional Hilbert space.

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T. Bermúdez, A. Martinón, H. Zaway. 2019-02-22. Some examples of $m$-isometries. https://arxiv.org/abs/1902.08492

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