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- W3009386985 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." @default.
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- W3009386985 date "2020-03-02" @default.
- W3009386985 modified "2023-09-24" @default.
- W3009386985 title "Some Examples of m-Isometries" @default.
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- W3009386985 doi "https://doi.org/10.1007/s00009-020-1501-0" @default.
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