On the classes of D-normal operators and D-quasi-normal operators on Hilbert space

Dana, M.; Yousefi, R.

doi:10.7153/oam-2018-12-29

Cited by 11 publications

(4 citation statements)

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“…2 leads to the simplification of the proofs of a number of results from [2,13]. Postponing this exercise for the time being, we start here with the following proposition which (contrary to the claim in [13,2]) proves that the classes [(n, m)DN ] and [(n, m)DQN ] of Hilbert space operators coincide.…”

Section: Resultsmentioning

confidence: 94%

On power Drazin normal and Drazin quasi-normal Hilbert space operators

Duggal¹,

Kim²

2019

Preprint

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A Drazin invertible Hilbert space operator T ∈ B(H), with Drazin inversewhere T 1 is similar to an invertible normal operator and T 0 is nilpotent. Using this representation, we have a keener look at the structure of [(n, m)DN ] and [(n, m)DQN ] operators. It is seen that T ∈ [(n, m)DN ] if and only if T ∈ [(n, m)DQN ], and if [T, X] = 0 for some operators X ∈ B(H) and T ∈ [(1, 1)DN ], then [T * d , X] = 0. Given simply polar operators S, T ∈ [(1, 1)DN ] and an operator A = T C 0 S ∈ B(H ⊕ H), A ∈ [(1, 1)DN ] if and only if C has a representation C = 0 ⊕ C 22 .

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Section: Resultsmentioning

confidence: 94%

On power Drazin normal and Drazin quasi-normal Hilbert space operators

Duggal¹,

Kim²

2019

Preprint

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“…These classes were firstly introduced by Dana and Yousefi [9]. From the definitions above, we can easily verify that:…”

Section: Preliminariesmentioning

confidence: 95%

D-hyponormal and D-quasi-hyponormal Operators

Mesbah

Messaoudene

2022

Comm. Math. Appl.

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“…In [4], the authors introduced the classes of D-normal operators and D-quasi-normal operators as a generalization of the classes of normal operators and quasi-normal operators, respectively. For more details we refer the reader to [5].…”

Section: Lemma 11 ([1]mentioning

confidence: 99%

On linear operators for which TTD is normal

Yousefi

Dana

2019

Filomat

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A Drazin invertible operator T ∈ B(H) is called skew D-quasi-normal operator if T * and TT D commute or equivalently TT D is normal. In this paper, firstly we give a list of conditions on an operator T, each of which is equivalent to T being skew D-quasi-normal. Furthermore, we obtain the matrix representation of these operators. We also develop some basic properties of such operators. Secondly we extend the Kaplansky theorem and the Fuglede-Putnam commutativity theorem for normal operators to skew D-quasi-normal matrices.

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On the classes of D-normal operators and D-quasi-normal operators on Hilbert space

Abstract: Abstract. The relations between these classes and some basic properties of these operators are studied in this study.Mathematics subject classification (2010): 47B15, 47B20, 47A15, 15A09.

Cited by 11 publications

References 0 publications

On power Drazin normal and Drazin quasi-normal Hilbert space operators

On power Drazin normal and Drazin quasi-normal Hilbert space operators

D-hyponormal and D-quasi-hyponormal Operators

On linear operators for which TTD is normal

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