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Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 4

Some results on higher orders quasi-isometries

Sid Ahmed Ould Ahmed Mahmoud
Adel Saddi
Khadija Gherairi
Pages
1315–1333
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Further, we define $n$-quasi strict $m$-isometric operators and prove their basic properties.

📌 3 Key Takeaways

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Objective & Hypothesis:The purpose of the present paper is to pursue further study of a class of linear bounded operators, known as $n$-quasi-$m$-isometric operators acting on an infinite complex separable Hilbert space ${\mathcal H}$.
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Key Findings & Data:However, we prove that if $T^r$ and $T^{r+1}$ are $n$-quasi-$m$-isometries for a positive integer $r$, then T is an $n$-quasi-$m$-isometric operator.
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Conclusion & Impact:Further, we define $n$-quasi strict $m$-isometric operators and prove their basic properties.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:m-isometry · strict m-isometry · n-quasi-m-isometry

Abstract

The purpose of the present paper is to pursue further study of a class of linear bounded operators, known as $n$-quasi-$m$-isometric operators acting on an infinite complex separable Hilbert space ${\mathcal H}$. We give an equivalent condition for any $T$ to be $n$-quasi-$m$-isometric operator. Using this result we prove that any power of an $n$-quasi-$m$-isometric operator is also an $n$-quasi-$m$-isometric operator. In general the converse is not true. However, we prove that if $T^r$ and $T^{r+1}$ are $n$-quasi-$m$-isometries for a positive integer $r$, then T is an $n$-quasi-$m$-isometric operator. We study the sum of an $n$-quasi-$m$-isometric operator with a nilpotent operator. We also study the product and tensor product of two $n$-quasi-$m$-isometries. Further, we define $n$-quasi strict $m$-isometric operators and prove their basic properties.

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Cite This Article

Mahmoud, S. A. O. A., Saddi, A., Gherairi, K. (2022). Some results on higher orders quasi-isometries. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 4, 1315–1333. https://ajindex.com/articles/529644

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