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

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.