2017
DOI: 10.2298/fil1707073c
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On [m,C]-isometric operators

Abstract: In this paper we introduce an [m;C]-isometric operator T on a complex Hilbert space H and study its spectral properties. We show that if T is an [m,C]-isometric operator and N is an n-nilpotent operator, respectively, then T + N is an [m + 2n ? 2,C]-isometric operator. Finally we give a short proof of Duggal?s result for tensor product of m-isometries and give a similar result for [m,C]-isometric operators.

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Cited by 15 publications
(17 citation statements)
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“…In [11], the authors showed that a power of an (m, C)-isometric operator is again a (m, C)-isometric operator. In the following theorem we show that this remains true for n-quasi-(m, C)-isometric operators.…”
Section: Resultsmentioning
confidence: 99%
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“…In [11], the authors showed that a power of an (m, C)-isometric operator is again a (m, C)-isometric operator. In the following theorem we show that this remains true for n-quasi-(m, C)-isometric operators.…”
Section: Resultsmentioning
confidence: 99%
“…The following lemma gives another condition for which an n-quasi-(m, C)-isometric operator became an n-quasi-(k, C)-isometric operator for k ≥ m. Proof. It is well known that Λ m+1 (T ) = T * Λ m (T )(CT C) − Λ m (T ) ( [11]). Under the assumptions that T is an n-quasi-(m, C)-isometric operator and satisfies T (CT C) = (CT C)T , it follows…”
Section: Resultsmentioning
confidence: 99%
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“…In [7], Chō, Ko, and Lee introduced (m, C)-isometric operators with conjugation C as follows: For an operator T ∈ B(H) and an integer m ≥ 1, T is said to be an (m, C)-isometric © The Author(s) 2019. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.…”
Section: Introductionmentioning
confidence: 99%
“…In [5], Chō et al introduced []-isometric operators with conjugation C as follows: For an operator and an integer , T is said to be an []-isometric operator if there exists some conjugation C such that …”
Section: Introductionmentioning
confidence: 99%