More on (α, β)‐Normal Operators in Hilbert Spaces

Eskandari, Rasoul; Mirzapour, F.; Morassaei, Ali

doi:10.1155/2012/204031

Cited by 3 publications

(3 citation statements)

References 5 publications

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“…In this framework, we show that many results from [7,8,12] remain true if we consider an additional semi-inner product defined by a positive semi-definite operator A. We are interested to introducing a new concept of normality in semi-Hilbertian spaces.…”

Section: Introduction and Preliminaries Resultsmentioning

confidence: 98%

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$(α,β)$-A-Normal Operators in Semi-Hilbertian Spaces

Benali¹,

Mahmoud²

2016

Preprint

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Let H be a Hilbert space and let A be a positive bounded operator on H. The semi-inner product u | v A := Au | v , u, v ∈ H induces a semi-norm . A on H. This makes H into a semi-Hilbertian space. In this paper we introduce and prove some proprieties of (α, β)-normal operators according to semi-Hilbertian space structures. Furthermore we state various inequalities between the A-operator norm and A-numerical radius of (α, β)-normal operators in semi Hilbertian spaces.

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Section: Introduction and Preliminaries Resultsmentioning

confidence: 98%

“…The following theorem presents a generalization of these results to (α, β)-A-normal. Our inspiration cames from [12,Theorem 2.5].…”

Section: Inequalities Involving A-operator Norms and A-numerical Radi...mentioning

confidence: 99%

$(α,β)$-A-Normal Operators in Semi-Hilbertian Spaces

Benali¹,

Mahmoud²

2016

Preprint

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“…For α 1, we observe that T * is hyponormal and for β 1, we obtain that T is hyponormal. Interested readers can nd more details on (α, β)-normal operators in [4][5][6][7][8][9]. e concept of p-(α, β)-normal operators was introduced by Senthilkumar and Shanthi [10].…”

Section: Introductionmentioning

confidence: 99%

$(α, β)$ -Normal Operators in Several Variables

Mahmoud

Himadan

Sarosh

2022

Mathematical Problems in Engineering

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We consider an extension of the concept of α , β -normal operators in single variable operator to tuples of operators, similar to those extensions of the concepts of normality to joint normality, hyponormality to joint hyponormality, and quasi-hyponormality to joint quasi-hyponormality.

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