Locally Strong Majorization and Commutativity in varvec{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.