Extensions of Kadison’s inequality on positive linear maps

Abstract: Let be a unital -algebra, the algebra of all bounded linear operators on a Hilbert space , and the set of all positive linear maps from to . The well-known Kadison’s inequality on unital positive linear maps is said that, if and is unital, then for each Hermitian . This paper is to consider the extensions of Kadison’s inequality, some inequalities for unital are obtained which generalize Furuta’s result, and a complement to a result of Bourin and Ricard is provided. [Copyright &y& Elsevier]