Bombieri-Type Inequalities and Their Applications in Semi-Hilbert Spaces
This paper presents new results related to Bombieri’s generalization of Bessel’s inequality in a semi-inner product space induced by a positive semidefinite operator <i>A</i>. Specifically, we establish new inequalities that generalize the classical Bessel inequality and extend previous...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/6/522 |
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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 | This paper presents new results related to Bombieri’s generalization of Bessel’s inequality in a semi-inner product space induced by a positive semidefinite operator <i>A</i>. Specifically, we establish new inequalities that generalize the classical Bessel inequality and extend previous results in this area. Furthermore, our findings have applications to the study of operators on positive semidefinite inner product spaces, also known as semi-Hilbert spaces, and contribute to a deeper understanding of their properties and applications. Our work has implications for various fields, including functional analysis and operator theory. |
| first_indexed | 2024-03-11T02:46:48Z |
| format | Article |
| id | doaj.art-6fb0df034c8243c197bdc0002620fe15 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T02:46:48Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-6fb0df034c8243c197bdc0002620fe152023-11-18T09:16:15ZengMDPI AGAxioms2075-16802023-05-0112652210.3390/axioms12060522Bombieri-Type Inequalities and Their Applications in Semi-Hilbert SpacesNajla Altwaijry0Silvestru Sever Dragomir1Kais Feki2Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaMathematics, College of Sport, Health and Engineering, Victoria University, P.O. Box 14428, Melbourne City, VIC 8001, AustraliaFaculty of Economic Sciences and Management of Mahdia, University of Monastir, Mahdia 5111, TunisiaThis paper presents new results related to Bombieri’s generalization of Bessel’s inequality in a semi-inner product space induced by a positive semidefinite operator <i>A</i>. Specifically, we establish new inequalities that generalize the classical Bessel inequality and extend previous results in this area. Furthermore, our findings have applications to the study of operators on positive semidefinite inner product spaces, also known as semi-Hilbert spaces, and contribute to a deeper understanding of their properties and applications. Our work has implications for various fields, including functional analysis and operator theory.https://www.mdpi.com/2075-1680/12/6/522positive semidefinite operatorbombieri inequalityjoint <i>A</i>-numerical radiuseuclidean <i>A</i>-seminorminequalities |
| spellingShingle | Najla Altwaijry Silvestru Sever Dragomir Kais Feki Bombieri-Type Inequalities and Their Applications in Semi-Hilbert Spaces Axioms positive semidefinite operator bombieri inequality joint <i>A</i>-numerical radius euclidean <i>A</i>-seminorm inequalities |
| title | Bombieri-Type Inequalities and Their Applications in Semi-Hilbert Spaces |
| title_full | Bombieri-Type Inequalities and Their Applications in Semi-Hilbert Spaces |
| title_fullStr | Bombieri-Type Inequalities and Their Applications in Semi-Hilbert Spaces |
| title_full_unstemmed | Bombieri-Type Inequalities and Their Applications in Semi-Hilbert Spaces |
| title_short | Bombieri-Type Inequalities and Their Applications in Semi-Hilbert Spaces |
| title_sort | bombieri type inequalities and their applications in semi hilbert spaces |
| topic | positive semidefinite operator bombieri inequality joint <i>A</i>-numerical radius euclidean <i>A</i>-seminorm inequalities |
| url | https://www.mdpi.com/2075-1680/12/6/522 |
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