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.
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Niezgoda, M. Locally Strong Majorization and Commutativity in \(\varvec{C^{*}}\)-Algebras with Applications. Results Math 74, 46 (2019). https://doi.org/10.1007/s00025-019-0956-4
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DOI: https://doi.org/10.1007/s00025-019-0956-4