Sherman type theorem on $C^{\ast}$ -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. m i=1 s ij = 1 for j = 1, . . . , n. An m × n real matrix S = (s ij ) is called row-stochastic if s ij ≥ 0 for i = 1, . . . , m, j = 1, . . . , n, and all row sums of S are

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

“…Theorem A ( [14,Corollary 3.4]). Let f : J → R be an operator convex function on interval J ⊂ R. Let A and B be unital C * -algebras.…”