No abstract

Let A, B be positive operators on a Hilbert space with 0 < m ≤ A, B ≤ M . Then for every unital positive linear map Φ,where A B is the geometric mean and K(h) = (h + 1) 2 /(4h) with h = M/m.

We improve the operator Kantorovich inequality as follows: Let A be a positive operator on a Hilbert space with 0 < m ≤ A ≤ M . Then for every unital positive linear map Φ,As a consequence,

Abstract. Two new inequalities are proved for sector matrices. The first one complements a recent result in [Oper. Matrices, 8 (2014) 1143-1148; the second one is an analogue of the AM-GM inequality, where the geometric mean for two sector matrices was introduced in [Linear Multilinear Algebra 63 (2015) 296-301]. As an application of the second inequality, we present similar inequalities for singular values or norms.Mathematics subject classification (2010): 15A45, 15A42, 47A30.