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Some Examples of m -Isometries
Mediterranean Journal of Mathematics ( IF 1.1 ) Pub Date : 2020-03-02 , DOI: 10.1007/s00009-020-1501-0
Teresa Bermúdez , Antonio Martinón , Hajer Zaway

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 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 a given m-isometry, using ideas of Aleman and Suciu (Integr Equ Oper Theory 85:259–287, 2016, Proposition 5.2) on infinite dimensional Hilbert space.

中文翻译:

m -Isometries的一些示例

我们获得了单位圆上的可允许集合,它是n个有限维希尔伯特空间上严格m等距的谱。此属性可以更好地显示m等轴测图的光谱。我们确定\(\ mathbb {R} ^ 2 \)上仅有的m个等式是3个等式和由\(\ pm I + Q \)给出的等式,其中Q是幂等算子。此外,在真实的希尔伯特空间上,我们得到m个等距保留了体积。另外,我们提出了一种使用给定m构造严格的\(((m + 1)\)- isometry的方法-等距,使用Aleman和Suciu(Integr Equ Oper Theory 85:259–287,2016,命题5.2)关于无限维希尔伯特空间的思想。
更新日期:2020-03-02
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