Further Inequalities for the Weighted Numerical Radius of Operators

Najla Altwaijry (), Kais Feki and Nicuşor Minculete
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Najla Altwaijry: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Kais Feki: Faculty of Economic Sciences and Management of Mahdia, University of Monastir, Mahdia 5111, Tunisia
Nicuşor Minculete: Department of Mathematics and Computer Science, Transilvania University of Brasov, 500091 Brasov, Romania

Mathematics, 2022, vol. 10, issue 19, 1-17

Abstract: This paper deals with the so-called A -numerical radius associated with a positive (semi-definite) bounded linear operator A acting on a complex Hilbert space H . Several new inequalities involving this concept are established. In particular, we prove several estimates for 2 × 2 operator matrices whose entries are A -bounded operators. Some of the obtained results cover and extend well-known recent results due to Bani-Domi and Kittaneh. In addition, several improvements of the generalized Kittaneh estimates are obtained. The inequalities given by Feki in his work represent a generalization of the inequalities given by Kittaneh. Some refinements of the inequalities due to Feki are also presented.

Keywords: positive operator; A -numerical radius; 2×2-operator matrix; A -adjoint operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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