Operator inequalities of Jensen type
M. S. Moslehian ; J. Mićić ; M. Kian
Topological Algebra and its Applications, Tome 1 (2013), p. 9-21 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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 [...]

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:266947 
@article{bwmeta1.element.doi-10_2478_taa-2013-0002,
     author = {M. S. Moslehian and J. Mi\'ci\'c and M. Kian},
     title = {Operator inequalities of Jensen type},
     journal = {Topological Algebra and its Applications},
     volume = {1},
     year = {2013},
     pages = {9-21},
     zbl = {06213277},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_taa-2013-0002}
}

M. S. Moslehian; J. Mićić; M. Kian. Operator inequalities of Jensen type. Topological Algebra and its Applications, Tome 1 (2013) pp. 9-21. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_taa-2013-0002/

[1] T. Ando and X. Zhan, Norm inequalities related to operator monotone functions, Math. Ann. 315 (1999), 771-780. | Zbl 0941.47004

[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. | Zbl 1135.47012

[4] M. Kian and M.S. Moslehian, Operator inequalities related to Q-class functions, Math. Slovaca, (to appear). | Zbl 06443661

[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. | Zbl 1105.47017

[6] J. Micic, Z. Pavic and J. Pecaric, Jensen’s inequality for operators without operator convexity, Linear Algebra Appl. 434 (2011), 1228-1237.[WoS] | Zbl 1216.47026

[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] | Zbl 1300.47024

[8] M.S. Moslehian, Operator extensions of Hua’s inequality, Linear Algebra Appl. 430 (2009), no. 4, 1131-1139.[WoS] | Zbl 1179.47018

[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] | Zbl 1301.47027

[10] M.S. Moslehian and H. Najafi. Around operator monotone functions, Integral Equations Operator Theory 71 (2011), 575-582. | Zbl 1272.47026

[11] M. Uchiyama, Subadditivity of eigenvalue sums, Proc. Amer. Math. Soc. 134 (2006), 1405-1412. | Zbl 1089.47010