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