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Geometric properties for a class of deformed trace functions
Published 24 Jul 2023 in math-ph and math.MP | (2307.13097v5)
Abstract: We investigate geometric properties of a class of trace functions expressed in terms of the deformed logarithmic and exponential functions. These trace functions and their properties may be of independent interest. We use them in particular to extend earlier results of Epstein, Hiai, Carlen and Lieb.
- T. Ando. Concavity of certain maps of positive definite matrices and applications to Hadamard products. Linear Algebra Appl., 26:203–241, 1979.
- Convex Optimization. Cambridge University Press, 2004.
- A Minkowsky type trace inequality and strong subadditivity of quantum entropy II: Convexity and concavity. Lett. Math. Phys., 83:107–126, 2008.
- H. Epstein. Remarks on two theorems of E. Lieb. Comm. Math. Phys., 31:317–325, 1973.
- Eric A Carlen et al. Inequalities for quantum divergences and the audenaert-datta conjecture. J. Phys. A: Math. Theor., 51:483001, 2018.
- Differential analysis of matrix convex functions II. Journal of Inequalities in Pure and Applied Mathematics, 10(2):5 pp., 2009.
- Fumio Hiai. Concavity of certain matrix trace and norm functions. Linear Algebra and Its Applications, 439:1568–1589, 2013.
- E. Lieb. Convex trace functions and the Wigner-Yanase-Dyson conjecture. Advances in Math., 11:267–288, 1973.
- Variational representations related to tsallis relative entropy. Letters in Mathematical Physics, 110:2203–2220, 2020.
- C. Tsallis. Nonadditive entropy and nonextensive statistical mechanics - an overview after 20 years. Brazilian Journal of Physics, 39(2A):337–356, 2009.
- Haonan Zhang. From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture. Advances in Mathematics, 365:107053, 2020.
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