On n-quasi- [m,C] $[m,C]$-isometric operators

Abstract For positive integers m and n, an operator T∈B(H) $T \in B ( H )$ is said to be an n-quasi- [m,C] $[m,C]$-isometric operator if there exists some conjugation C such that T∗n(∑j=0m(−1)j(mj)CTm−jC.Tm−j)Tn=0 . In this paper, some basic structural properties of n-quasi- [m,C] $[m,C]$-isometric...

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Main Author:	Junli Shen
Format:	Article
Language:	English
Published:	SpringerOpen 2019-12-01
Series:	Journal of Inequalities and Applications
Subjects:	n-quasi- [ m , C ] $[m,C]$ -isometric operator Perturbation Nilpotent operator
Online Access:	https://doi.org/10.1186/s13660-019-2268-3

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spelling	doaj-eaff9c95eb16430b9b90a3d8672f0a312020-12-13T12:02:44ZengSpringerOpenJournal of Inequalities and Applications1029-242X2019-12-01201911910.1186/s13660-019-2268-3On n-quasi- [m,C] $[m,C]$-isometric operatorsJunli Shen0College of Computer and Information Technology, Henan Normal UniversityAbstract For positive integers m and n, an operator T∈B(H) $T \in B ( H )$ is said to be an n-quasi- [m,C] $[m,C]$-isometric operator if there exists some conjugation C such that T∗n(∑j=0m(−1)j(mj)CTm−jC.Tm−j)Tn=0 . In this paper, some basic structural properties of n-quasi- [m,C] $[m,C]$-isometric operators are established with the help of operator matrix representation. As an application, we obtain that a power of an n-quasi- [m,C] $[m,C]$-isometric operator is again an n-quasi- [m,C] $[m,C]$-isometric operator. Moreover, we show that the class of n-quasi- [m,C] $[m,C]$-isometric operators is norm closed. Finally, we examine the stability of n-quasi- [m,C] $[m,C]$-isometric operator under perturbation by nilpotent operators commuting with T.https://doi.org/10.1186/s13660-019-2268-3n-quasi- [ m , C ] $[m,C]$ -isometric operatorPerturbationNilpotent operator
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Junli Shen
spellingShingle	Junli Shen On n-quasi- [m,C] $[m,C]$-isometric operators Journal of Inequalities and Applications n-quasi- [ m , C ] $[m,C]$ -isometric operator Perturbation Nilpotent operator
author_facet	Junli Shen
author_sort	Junli Shen
title	On n-quasi- [m,C] $[m,C]$-isometric operators
title_short	On n-quasi- [m,C] $[m,C]$-isometric operators
title_full	On n-quasi- [m,C] $[m,C]$-isometric operators
title_fullStr	On n-quasi- [m,C] $[m,C]$-isometric operators
title_full_unstemmed	On n-quasi- [m,C] $[m,C]$-isometric operators
title_sort	on n-quasi- [m,c] $[m,c]$-isometric operators
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1029-242X
publishDate	2019-12-01
description	Abstract For positive integers m and n, an operator T∈B(H) $T \in B ( H )$ is said to be an n-quasi- [m,C] $[m,C]$-isometric operator if there exists some conjugation C such that T∗n(∑j=0m(−1)j(mj)CTm−jC.Tm−j)Tn=0 . In this paper, some basic structural properties of n-quasi- [m,C] $[m,C]$-isometric operators are established with the help of operator matrix representation. As an application, we obtain that a power of an n-quasi- [m,C] $[m,C]$-isometric operator is again an n-quasi- [m,C] $[m,C]$-isometric operator. Moreover, we show that the class of n-quasi- [m,C] $[m,C]$-isometric operators is norm closed. Finally, we examine the stability of n-quasi- [m,C] $[m,C]$-isometric operator under perturbation by nilpotent operators commuting with T.
topic	n-quasi- [ m , C ] $[m,C]$ -isometric operator Perturbation Nilpotent operator
url	https://doi.org/10.1186/s13660-019-2268-3
work_keys_str_mv	AT junlishen onnquasimcmcisometricoperators
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On n-quasi- [m,C] $[m,C]$-isometric operators

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