Operator inequalities of Jensen type

• Autorzy: M. S. Moslehian , J. Mićić , M. Kian
• Języki publikacji: EN

Abstrakty

EN

We present some generalized Jensen type operator inequalities involving sequences of self-adjoint operators. Among other things, we prove that if f : [0;1) → ℝ is a continuous convex function with f(0) ≤ 0, then [...] for all operators Ci such that [...] (i=1 , ... , n) for some scalar M ≥ 0, where [...] and [...]

Słowa kluczowe

EN

convex function; positive linear map; Jensen-Mercer operator inequality; Petrovic operator inequality

Kategorie tematyczne

• 15A60: Norms of matrices, numerical range, applications of functional analysis to matrix theory
• 47A63: Operator inequalities
• 47A64: Operator means, shorted operators, etc.

• Wydawca: De Gruyter Open
• Czasopismo: Topological Algebra and its Applications
• Rocznik: 2013
• Tom: 1
• Strony: 9-21

Daty

zaakceptowano

2012-03-18

otrzymano

2012-10-07

online

2013-07-06

Twórcy

autor

M. S. Moslehian

• Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran

autor

J. Mićić

• Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10000 Zagreb, Croatia

autor

M. Kian

• Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran

Bibliografia

• [1] T. Ando and X. Zhan, Norm inequalities related to operator monotone functions, Math. Ann. 315 (1999), 771-780.
• [2] K. M.R. Audenaert and J.S. Aujla On norm sub-additivity and super-additivity inequalities for concave and convexfunctions , arXiv:1012.2254v2.[WoS]
• [3] T. Furuta, J. Micic Hot, J. Pecaric and Y. Seo, Mond-Pecaric Method in Operator Inequalities, Zagreb, Element, 2005.
• [4] M. Kian and M.S. Moslehian, Operator inequalities related to Q-class functions, Math. Slovaca, (to appear).
• [5] A. Matkovic, J. Pecaric and I. Peric, A variant of Jensen’s inequality of Mercer’s type for operators with applications, Linear Algebra Appl. 418 (2006), 551-564.
• [6] J. Micic, Z. Pavic and J. Pecaric, Jensen’s inequality for operators without operator convexity, Linear Algebra Appl. 434 (2011), 1228-1237.[WoS]
• [7] J. Micic, J. Pecaric and J. Peric, Refined Jensen’s operator inequality with condition on spectra, Oper. Matrices 7 (2013), 293-308.[WoS][Crossref]
• [8] M.S. Moslehian, Operator extensions of Hua’s inequality, Linear Algebra Appl. 430 (2009), no. 4, 1131-1139.[WoS]
• [9] M.S. Moslehian, J. Micic and M. Kian, An operator inequality and its consequences, Linear Algebra Appl. DOI: 10.1016/j.laa.2012.08.005.[Crossref][WoS]
• [10] M.S. Moslehian and H. Najafi. Around operator monotone functions, Integral Equations Operator Theory 71 (2011), 575-582.
• [11] M. Uchiyama, Subadditivity of eigenvalue sums, Proc. Amer. Math. Soc. 134 (2006), 1405-1412.

Identyfikatory

DOI

10.2478/taa-2013-0002