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Results in Mathematics

, 74:46 | Cite as

Locally Strong Majorization and Commutativity in \(\varvec{C^{*}}\)-Algebras with Applications

  • Marek NiezgodaEmail author
Open Access
Article
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Abstract

In this paper, we introduce the notion of locally strong majorization for self-adjoint operators in a \( C^*\)-algebra. This allows, by using a Sherman type theorem for operators, to prove a Hardy–Littlewood–Pólya–Karamata like theorem. We show the role of commutativity of self-adjoint operators in such problems. We study operator inequalities of Moslehian–Micić–Kian, Mercer and Dragomir types.

Keywords

Self-adjoint operator operator convex function positive linear map majorization column stochastic matrix 

Mathematics Subject Classification

47A63 15A27 26D15 26B25 

Notes

Acknowledgements

The author would like to thank anonymous referees for giving valuable comments that helped to improve the manuscript.

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Copyright information

© The Author(s) 2019

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Computer ScienceUniversity of Life Sciences in LublinLublinPoland

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