Further Inequalities for the Weighted Numerical Radius of Operators
This paper deals with the so-called <i>A</i>-numerical radius associated with a positive (semi-definite) bounded linear operator <i>A</i> acting on a complex Hilbert space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline...
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| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/19/3576 |
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| author | Najla Altwaijry Kais Feki Nicuşor Minculete |
| author_facet | Najla Altwaijry Kais Feki Nicuşor Minculete |
| author_sort | Najla Altwaijry |
| collection | DOAJ |
| description | This paper deals with the so-called <i>A</i>-numerical radius associated with a positive (semi-definite) bounded linear operator <i>A</i> acting on a complex Hilbert space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">H</mi></semantics></math></inline-formula>. Several new inequalities involving this concept are established. In particular, we prove several estimates for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mo>×</mo><mn>2</mn></mrow></semantics></math></inline-formula> operator matrices whose entries are <i>A</i>-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. |
| first_indexed | 2024-03-09T21:27:48Z |
| format | Article |
| id | doaj.art-aa0d3dc7328e4a09afeb138ff41aeb18 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T21:27:48Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-aa0d3dc7328e4a09afeb138ff41aeb182023-11-23T21:03:53ZengMDPI AGMathematics2227-73902022-09-011019357610.3390/math10193576Further Inequalities for the Weighted Numerical Radius of OperatorsNajla Altwaijry0Kais Feki1Nicuşor Minculete2Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaFaculty of Economic Sciences and Management of Mahdia, University of Monastir, Mahdia 5111, TunisiaDepartment of Mathematics and Computer Science, Transilvania University of Brasov, 500091 Brasov, RomaniaThis paper deals with the so-called <i>A</i>-numerical radius associated with a positive (semi-definite) bounded linear operator <i>A</i> acting on a complex Hilbert space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">H</mi></semantics></math></inline-formula>. Several new inequalities involving this concept are established. In particular, we prove several estimates for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mo>×</mo><mn>2</mn></mrow></semantics></math></inline-formula> operator matrices whose entries are <i>A</i>-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.https://www.mdpi.com/2227-7390/10/19/3576positive operator<i>A</i>-numerical radius2×2-operator matrix<i>A</i>-adjoint operator |
| spellingShingle | Najla Altwaijry Kais Feki Nicuşor Minculete Further Inequalities for the Weighted Numerical Radius of Operators Mathematics positive operator <i>A</i>-numerical radius 2×2-operator matrix <i>A</i>-adjoint operator |
| title | Further Inequalities for the Weighted Numerical Radius of Operators |
| title_full | Further Inequalities for the Weighted Numerical Radius of Operators |
| title_fullStr | Further Inequalities for the Weighted Numerical Radius of Operators |
| title_full_unstemmed | Further Inequalities for the Weighted Numerical Radius of Operators |
| title_short | Further Inequalities for the Weighted Numerical Radius of Operators |
| title_sort | further inequalities for the weighted numerical radius of operators |
| topic | positive operator <i>A</i>-numerical radius 2×2-operator matrix <i>A</i>-adjoint operator |
| url | https://www.mdpi.com/2227-7390/10/19/3576 |
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