Sherman type theorem on C*-algebras

Abstract

In this paper, a new definition of majorization for $C^{*}$-algebras is introduced. Sherman’s inequality is extended to self-adjoint operators and positive linear maps by applying the method of premajorization used for comparing two tuples of objects. A general result in a matrix setting is established. Special cases of the main theorem are studied. In particular, a HLPK-type inequality is derived.