In this paper, a new definition of majorization for -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.
"Sherman type theorem on -algebras." Ann. Funct. Anal. 8 (4) 425 - 434, November 2017. https://doi.org/10.1215/20088752-2017-0007