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## Some results on higher orders quasi-isometries

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.
m-isometry, strict m-isometry, n-quasi-m-isometry
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Primary Language en Mathematics Mathematics Orcid: 0000-0002-6891-7849Author: Sid Ahmed OULD AHMED MAHMOUD (Primary Author)Institution: Jouf UniversityCountry: Saudi Arabia Orcid: 0000-0001-5034-3958Author: Adel SADDİ Institution: Gabes UniversityCountry: Tunisia Orcid: 0000-0002-5269-8186Author: Khadija GHERAİRİ Institution: Gabes UniversityCountry: Tunisia Publication Date : August 6, 2020
 Bibtex @research article { hujms532964, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1315 - 1333}, doi = {10.15672/hujms.532964}, title = {Some results on higher orders quasi-isometries}, key = {cite}, author = {Ould Ahmed Mahmoud, Sid Ahmed and Saddi̇, Adel and Gherai̇ri̇, Khadija} } APA Ould Ahmed Mahmoud, S , Saddi̇, A , Gherai̇ri̇, K . (2020). Some results on higher orders quasi-isometries . Hacettepe Journal of Mathematics and Statistics , 49 (4) , 1315-1333 . DOI: 10.15672/hujms.532964 MLA Ould Ahmed Mahmoud, S , Saddi̇, A , Gherai̇ri̇, K . "Some results on higher orders quasi-isometries" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1315-1333 Chicago Ould Ahmed Mahmoud, S , Saddi̇, A , Gherai̇ri̇, K . "Some results on higher orders quasi-isometries". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1315-1333 RIS TY - JOUR T1 - Some results on higher orders quasi-isometries AU - Sid Ahmed Ould Ahmed Mahmoud , Adel Saddi̇ , Khadija Gherai̇ri̇ Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.532964 DO - 10.15672/hujms.532964 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1315 EP - 1333 VL - 49 IS - 4 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.532964 UR - https://doi.org/10.15672/hujms.532964 Y2 - 2019 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Some results on higher orders quasi-isometries %A Sid Ahmed Ould Ahmed Mahmoud , Adel Saddi̇ , Khadija Gherai̇ri̇ %T Some results on higher orders quasi-isometries %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 4 %R doi: 10.15672/hujms.532964 %U 10.15672/hujms.532964 ISNAD Ould Ahmed Mahmoud, Sid Ahmed , Saddi̇, Adel , Gherai̇ri̇, Khadija . "Some results on higher orders quasi-isometries". Hacettepe Journal of Mathematics and Statistics 49 / 4 (August 2020): 1315-1333 . https://doi.org/10.15672/hujms.532964 AMA Ould Ahmed Mahmoud S , Saddi̇ A , Gherai̇ri̇ K . Some results on higher orders quasi-isometries. Hacettepe Journal of Mathematics and Statistics. 2020; 49(4): 1315-1333. Vancouver Ould Ahmed Mahmoud S , Saddi̇ A , Gherai̇ri̇ K . Some results on higher orders quasi-isometries. Hacettepe Journal of Mathematics and Statistics. 2020; 49(4): 1315-1333.

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