$ n $-quasi-$ A $-$ (m, q) $-isometry on a Banach space

Khadija Gherairi; Zayd Hajjej; Haiyan Li; Hedi Regeiba; Khadija Gherairi; Zayd Hajjej; Haiyan Li; Hedi Regeiba

doi:10.3934/math.20231448

AIMS Mathematics

2023, Volume 8, Issue 12: 28308-28321. doi: 10.3934/math.20231448

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$ n $-quasi-$ A $-$ (m, q) $-isometry on a Banach space

1.
Laboratory of Mathematics and Applications, College of Sciencs, Gabes University, Tunisia
2.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
3.
College of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China

Received: 04 August 2023 Revised: 25 September 2023 Accepted: 07 October 2023 Published: 17 October 2023
MSC : 47B99, 47A05

In this paper, we introduce the class of $ n $-quasi-$ A $-$ (m, q) $-isometry operators on a Banach space $ X $, which represents a generalization of the $ n $-quasi-$ (m, q) $-isometry on a Banach space and the $ n $-quasi-$ (A, m) $-isometry on a Hilbert space. After giving some basic properties of this class of operators, we study the product and the power of such operators in this class.
- $ m $-isometry,
- $ (m, q) $-isometry,
- $ n $-quasi-$ A $-$ (m, q) $-isometry
Citation: Khadija Gherairi, Zayd Hajjej, Haiyan Li, Hedi Regeiba. $ n $-quasi-$ A $-$ (m, q) $-isometry on a Banach space[J]. AIMS Mathematics, 2023, 8(12): 28308-28321. doi: 10.3934/math.20231448

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Abstract

In this paper, we introduce the class of $ n $-quasi-$ A $-$ (m, q) $-isometry operators on a Banach space $ X $, which represents a generalization of the $ n $-quasi-$ (m, q) $-isometry on a Banach space and the $ n $-quasi-$ (A, m) $-isometry on a Hilbert space. After giving some basic properties of this class of operators, we study the product and the power of such operators in this class.

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