Publication Date
9-1-2024
Document Type
Article
Publication Title
Symmetry
Volume
16
Issue
9
DOI
10.3390/sym16091176
Abstract
The original Choi–Davis–Jensen’s inequality, known for its extensive applications in various scientific and engineering fields, has inspired researchers to pursue its generalizations. In this study, we extend the Choi–Davis–Jensen’s inequality by introducing a nonlinear map instead of a normalized linear map and generalize the concept of operator convex functions to include any continuous function defined within a compact region. Notably, operators can be matrices with structural symmetry, enhancing the scope and applicability of our results. The Stone–Weierstrass theorem and the Kantorovich function play crucial roles in the formulation and proof of these generalized Choi–Davis–Jensen’s inequalities. Furthermore, we demonstrate an application of this generalized inequality in the context of statistical physics.
Funding Number
G2023132005L
Funding Sponsor
Institute for Information Industry, Ministry of Science and Technology, Taiwan
Keywords
Choi–Davis–Jensen’s inequality, Kantorovich function, Loewner ordering, Stone–Weierstrass theorem
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Applied Data Science
Recommended Citation
Shih Yu Chang and Yimin Wei. "Generalized Choi–Davis–Jensen’s Operator Inequalities and Their Applications" Symmetry (2024). https://doi.org/10.3390/sym16091176
