Inequalities Involving A-Numerical Radius and Operator A-Norm for a Class of Operators Related to α,β−A-Normal Operators

In this article, we introduce and study a new class of operators, larger than α,β−A-normal operators and different than α,β−A-normal operators, named m-quasi-α,β−A-normal operators. Considering the semi-inner product induced by a positive operator A, the m-quasi-α,β−A-normal operators turn into a ge...

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Bibliographic Details
Published inJournal of mathematics (Hidawi) Vol. 2022
Main Authors Ould Ahmed Mahmoud, Sid Ahmed, Jah, Sidi Hamidou
Format Journal Article
LanguageEnglish
Published Cairo Hindawi 2022
Hindawi Limited
Wiley
Subjects
Hilbert space
Inequalities
Mathematics
Operators
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Summary:In this article, we introduce and study a new class of operators, larger than α,β−A-normal operators and different than α,β−A-normal operators, named m-quasi-α,β−A-normal operators. Considering the semi-inner product induced by a positive operator A, the m-quasi-α,β−A-normal operators turn into a generalization (for this new structure) of classical m-quasi-α,β-normal operators. Several results concerning properties of this kind of operators are presented in the paper. Several inequalities for the A-numerical radius and A-operator norm for members of this class are established.
ISSN:2314-4629
2314-4785
DOI:10.1155/2022/1506330