2014
DOI: 10.1155/2014/745479
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Perturbation ofm-Isometries by Nilpotent Operators

Abstract: We prove that ifTis anm-isometry on a Hilbert space andQann-nilpotent operator commuting withT, thenT+Qis a2n+m-2-isometry. Moreover, we show that a similar result form, q-isometries on Banach spaces is not true.

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Cited by 34 publications
(19 citation statements)
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“…In [2] the connection between Jordan operators and 3-symmetric operators was established in general. A sample of the more recent articles related to 3-isometries includes [3][4][5][6][7][8][9][10][11]15,16,18,20].…”
Section: An Operator T ∈ B(h) Is a 3-isometry Ifmentioning
confidence: 99%
“…In [2] the connection between Jordan operators and 3-symmetric operators was established in general. A sample of the more recent articles related to 3-isometries includes [3][4][5][6][7][8][9][10][11]15,16,18,20].…”
Section: An Operator T ∈ B(h) Is a 3-isometry Ifmentioning
confidence: 99%
“…In [12], it was showed that if S is an isometry on any Hilbert space and N is a nilpotent operator of order n commuting with S then the sum S + N is a strict (2n − 1)-isometry. This result has been generalized to m-isometries by several authors [26,11,22].…”
Section: Introductionmentioning
confidence: 77%
“…Very recently, researchers have been interested in algebraic properties, cyclicity and supercyclicity of m-isometries, among other things. See [28,24,14,16,15,18,13,12,26,11,22] and the references therein. It was showed by Agler, Helton and Stankus [4,Section 1.4] that any m-isometry T on a finite dimensional Hilbert space admits a decomposition T = S + N, where S is a unitary and N is a nilpotent operator satisfying SN = NS.…”
Section: Introductionmentioning
confidence: 99%
“…It is proved in [3] that every isometric N -Jordan operator is a strict (2N − 1)-isometry. Moreover, it is shown in [2] that if A is an m-isometry then A + Q is a (2N − m − 2)-isometry. Recently, such operators have been considered by several authors; for example, see [4,6] .…”
Section: Let H Be a Hilbert Space And B(h) Stands For The Space Of Almentioning
confidence: 99%