Some Results on the Classes of D-normal Operators and n-power D-normal Operators

Dana, M.; Yousefi, R.

doi:10.1007/s00025-018-0949-8

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Lemma 11 ([1]1

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2019

2024

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Cited by 7 publications

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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]. The class of skew D-quasi-normal operators was defined by Dana and Yousefi [6] as a generalization of the class of D-normal operators.…”

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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Section: Lemma 11 ([1]mentioning

confidence: 99%