Inequalities and Reverse Inequalities for the Joint <i>A</i>-Numerical Radius of Operators
In this paper, we aim to establish several estimates concerning the generalized Euclidean operator radius of <i>d</i>-tuples of <i>A</i>-bounded linear operators acting on a complex Hilbert space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML&qu...
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MDPI AG
2023-03-01
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| Online Access: | https://www.mdpi.com/2075-1680/12/3/316 |
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| author | Najla Altwaijry Silvestru Sever Dragomir Kais Feki |
| author_facet | Najla Altwaijry Silvestru Sever Dragomir Kais Feki |
| author_sort | Najla Altwaijry |
| collection | DOAJ |
| description | In this paper, we aim to establish several estimates concerning the generalized Euclidean operator radius of <i>d</i>-tuples of <i>A</i>-bounded linear operators 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>, which leads to the special case of the well-known <i>A</i>-numerical radius for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>. Here, <i>A</i> is a positive operator on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">H</mi></semantics></math></inline-formula>. Some inequalities related to the Euclidean operator <i>A</i>-seminorm of <i>d</i>-tuples of <i>A</i>-bounded operators are proved. In addition, under appropriate conditions, several reverse bounds for the <i>A</i>-numerical radius in single and multivariable settings are also stated. |
| first_indexed | 2024-03-11T06:56:34Z |
| format | Article |
| id | doaj.art-810cc327483f48a4b0414d3a33f7fca3 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T06:56:34Z |
| publishDate | 2023-03-01 |
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| spelling | doaj.art-810cc327483f48a4b0414d3a33f7fca32023-11-17T09:35:48ZengMDPI AGAxioms2075-16802023-03-0112331610.3390/axioms12030316Inequalities and Reverse Inequalities for the Joint <i>A</i>-Numerical Radius of OperatorsNajla Altwaijry0Silvestru Sever Dragomir1Kais Feki2Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaCollege of Engineering and Science, Victoria University, Melbourne, VIC 8000, AustraliaFaculty of Economic Sciences and Management of Mahdia, University of Monastir, Mahdia 5111, TunisiaIn this paper, we aim to establish several estimates concerning the generalized Euclidean operator radius of <i>d</i>-tuples of <i>A</i>-bounded linear operators 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>, which leads to the special case of the well-known <i>A</i>-numerical radius for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>. Here, <i>A</i> is a positive operator on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">H</mi></semantics></math></inline-formula>. Some inequalities related to the Euclidean operator <i>A</i>-seminorm of <i>d</i>-tuples of <i>A</i>-bounded operators are proved. In addition, under appropriate conditions, several reverse bounds for the <i>A</i>-numerical radius in single and multivariable settings are also stated.https://www.mdpi.com/2075-1680/12/3/316positive operatorjoint <i>A</i>-numerical radiusEuclidean operator <i>A</i>-seminormjoint operator <i>A</i>-seminorm |
| spellingShingle | Najla Altwaijry Silvestru Sever Dragomir Kais Feki Inequalities and Reverse Inequalities for the Joint <i>A</i>-Numerical Radius of Operators Axioms positive operator joint <i>A</i>-numerical radius Euclidean operator <i>A</i>-seminorm joint operator <i>A</i>-seminorm |
| title | Inequalities and Reverse Inequalities for the Joint <i>A</i>-Numerical Radius of Operators |
| title_full | Inequalities and Reverse Inequalities for the Joint <i>A</i>-Numerical Radius of Operators |
| title_fullStr | Inequalities and Reverse Inequalities for the Joint <i>A</i>-Numerical Radius of Operators |
| title_full_unstemmed | Inequalities and Reverse Inequalities for the Joint <i>A</i>-Numerical Radius of Operators |
| title_short | Inequalities and Reverse Inequalities for the Joint <i>A</i>-Numerical Radius of Operators |
| title_sort | inequalities and reverse inequalities for the joint i a i numerical radius of operators |
| topic | positive operator joint <i>A</i>-numerical radius Euclidean operator <i>A</i>-seminorm joint operator <i>A</i>-seminorm |
| url | https://www.mdpi.com/2075-1680/12/3/316 |
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