Generalized Choi-Davis-Jensen's Operator Inequalities and Their Applications
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929268499415040 |
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| author | Chang, Shih Yu Wei, Yimin |
| author_facet | Chang, Shih Yu Wei, Yimin |
| contents | The original Choi-Davis-Jensen's inequality, with its wide-ranging applications in diverse scientific and engineering fields, has motivated researchers to explore generalizations. In this study, we extend Davis-Choi-Jensen's inequality by considering a nonlinear map instead of a normalized linear map and generalize operator convex function to any continuous function defined in a compact region. The Stone-Weierstrass theorem and Kantorovich function are instrumental in formulating and proving generalized Choi-Davis-Jensen's inequalities. Additionally, we present an application of this generalized inequality in the context of statistical physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04892 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Choi-Davis-Jensen's Operator Inequalities and Their Applications Chang, Shih Yu Wei, Yimin Operator Algebras Mathematical Physics The original Choi-Davis-Jensen's inequality, with its wide-ranging applications in diverse scientific and engineering fields, has motivated researchers to explore generalizations. In this study, we extend Davis-Choi-Jensen's inequality by considering a nonlinear map instead of a normalized linear map and generalize operator convex function to any continuous function defined in a compact region. The Stone-Weierstrass theorem and Kantorovich function are instrumental in formulating and proving generalized Choi-Davis-Jensen's inequalities. Additionally, we present an application of this generalized inequality in the context of statistical physics. |
| title | Generalized Choi-Davis-Jensen's Operator Inequalities and Their Applications |
| topic | Operator Algebras Mathematical Physics |
| url | https://arxiv.org/abs/2403.04892 |