Generalized Operator Shannon Entropy and Related Operator Inequalities

被引：0
作者：
Ismail Nikoufar
Kenjiro Yanagi
机构：
[1] Payame Noor University,Department of Mathematics
[2] Josai University,Department of Mathematics
来源：
Iranian Journal of Science | 2023年 / 47卷
关键词：
Operator inequality; Operator Shannon-type inequality; Relative operator entropy; Generalized relative operator entropy; 47A63; 46L05; 46L60;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we investigate a notion of the relative operator entropy developing the theory started by Fujii and Kamei. We consider generalized operator Shannon entropy and give its upper and lower bounds under certain conditions. Our results generalize and extend various comparable results in the existing literature. As an application, we refine some inequalities concerning an inequality due to Furuta and a generalized operator version of Shannon inequality and its reverse one.
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页码：1379 / 1384
页数：5
相关论文
共 24 条
  • [1] Ebadian A(2011)Perspectives of matrix convex functions Proc Natl Acad Sci 108 7313-7314
  • [2] Nikoufar I(2009)A matrix convexity approach to some celebrated quantum inequalities Proc Natl Acad Sci USA 106 1006-1008
  • [3] Gordji ME(2004)Parametric extensions of Shannon inequality and its reverse one in Hilbert space operators Linear Algebra Appl 381 219-235
  • [4] Effros EG(1989)Relative operator entropy in noncommutative information theory Math Jpn 34 341-348
  • [5] Furuta T(2005)A note on operator inequalities of Tsallis relative operator entropy Linear Algebra Appl 407 19-31
  • [6] Fujii JI(2013)Operator entropy inequalities Colloq Math 130 159-168
  • [7] Kamei E(2016)Operator versions of Shannon type inequality Math Ineq Appl 19 359-367
  • [8] Furuichi S(2017)Bounds of generalized relative operator entropies Math Inequal Appl 20 1067-1078
  • [9] Yanagi K(2020)Improved operator inequalities of some relative operative entropies Positivity 24 241-251
  • [10] Kuriyama K(2020)Inequalities for the generalized Tsallis relative operator entropy Filomat 34 2713-2721
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