Operator inequalities of Jensen type

M. S. Moslehian; J. Mićić; M. Kian

Topological Algebra and its Applications (2013)

  • Volume: 1, page 9-21
  • ISSN: 2299-3231

Abstract

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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 [...]

How to cite

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M. S. Moslehian, J. Mićić, and M. Kian. "Operator inequalities of Jensen type." Topological Algebra and its Applications 1 (2013): 9-21. <http://eudml.org/doc/266947>.

@article{M2013,
abstract = {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 [...]},
author = {M. S. Moslehian, J. Mićić, M. Kian},
journal = {Topological Algebra and its Applications},
keywords = {convex function; positive linear map; Jensen-Mercer operator inequality; Petrovic operator inequality; Petrović operator inequality},
language = {eng},
pages = {9-21},
title = {Operator inequalities of Jensen type},
url = {http://eudml.org/doc/266947},
volume = {1},
year = {2013},
}

TY - JOUR
AU - M. S. Moslehian
AU - J. Mićić
AU - M. Kian
TI - Operator inequalities of Jensen type
JO - Topological Algebra and its Applications
PY - 2013
VL - 1
SP - 9
EP - 21
AB - 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 [...]
LA - eng
KW - convex function; positive linear map; Jensen-Mercer operator inequality; Petrovic operator inequality; Petrović operator inequality
UR - http://eudml.org/doc/266947
ER -

References

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  1. [1] T. Ando and X. Zhan, Norm inequalities related to operator monotone functions, Math. Ann. 315 (1999), 771-780. Zbl0941.47004
  2. [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. [3] T. Furuta, J. Micic Hot, J. Pecaric and Y. Seo, Mond-Pecaric Method in Operator Inequalities, Zagreb, Element, 2005. Zbl1135.47012
  4. [4] M. Kian and M.S. Moslehian, Operator inequalities related to Q-class functions, Math. Slovaca, (to appear). Zbl06443661
  5. [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. Zbl1105.47017
  6. [6] J. Micic, Z. Pavic and J. Pecaric, Jensen’s inequality for operators without operator convexity, Linear Algebra Appl. 434 (2011), 1228-1237.[WoS] Zbl1216.47026
  7. [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] Zbl1300.47024
  8. [8] M.S. Moslehian, Operator extensions of Hua’s inequality, Linear Algebra Appl. 430 (2009), no. 4, 1131-1139.[WoS] Zbl1179.47018
  9. [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] Zbl1301.47027
  10. [10] M.S. Moslehian and H. Najafi. Around operator monotone functions, Integral Equations Operator Theory 71 (2011), 575-582. Zbl1272.47026
  11. [11] M. Uchiyama, Subadditivity of eigenvalue sums, Proc. Amer. Math. Soc. 134 (2006), 1405-1412. Zbl1089.47010

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