A perspective approach for characterization of Lieb concavity theorem

• Autorzy: Nikoufar I.
• Języki publikacji: EN

Abstrakty

EN

Lieb’s extension theorem holds for generalized p + q ∈ [0, 1] and Ando convexity theorem holds for q – r > 1. In this paper, we give a complete characterization for concavity or convexity of Lieb well known theorem in the case where p + q ≥ 1 or p +q ≤ 0. We also characterize some auxiliary results including Ando theorem for q – r ≤ 1.

Słowa kluczowe

EN

perspective function; generalized perspective function; matrix convex function

PL

funkcja perspektywy; macierz funkcji wypukłej

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2016
• Tom: Vol. 49, nr 4
• Strony: 463--469
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Nikoufar I.

• Department of Mathematics, Payame Noor University, P.O. BOX 19395-3697 Tehran, Iran

Bibliografia

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• [2] T. Ando, Concavity of certain maps on positive definite matrices and applications to Hadamard products, Linear Algebra Appl. 26 (1979), 203–241.
• [3] J. S. Aujla, A simple proof of Lieb concavity theorem, J. Math. Phys. 52, 043505 (2011), 3 pages. doi:10.1063/1.3573594
• [4] R. Bhatia, Matrix Analysis, Graduate Texts in Mathematics 169, Springer, New York, 1997.
• [5] A. Ebadian, I. Nikoufar, M. Eshagi Gordji, Perspectives of matrix convex functions, Proc. Nat. Acad. Sci. U.S.A. 108(18) (2011), 7313–7314.
• [6] E. G. Effros, A matrix convexity approach to some celebrated quantum inequalities, Proc. Nat. Acad. Sci. U.S.A. 106(4) (2009), 1006–1008.
• [7] F. Hansen, G. Pedersen, Jensen’s operator inequality, Bull. London Math. Soc. 35 (2003), 553–564.
• [8] F. Kubo, T. Ando, Means of positive linear operators, Math. Ann. 246 (1979–1980), 205–224.
• [9] E. Lieb, Convex trace functions and the Wigner–Yanase–Dyson conjecture, Adv. Math. 11 (1973), 267–288.
• [10] I. Nikoufar, On operator inequalities of some relative operator entropies, Adv. Math. 259 (2014), 376–383.
• [11] I. Nikoufar, A. Ebadian, M. Eshagi Gordji, The simplest proof of Lieb concavity theorem, Adv. Math. 248 (2013), 531–533.
• [12] E. P. Wigner, M. M. Yanase, Information contents of distributions, Proc. Nat. Acad. Sci. U.S.A. 49 (1963), 910–918.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.