Some inequalities for interpolational operator means

Abstract

Using the properties of geometric mean, we shall show for any 0 ≤ α, β ≤ 1,whenever f is a non-negative operator log-convex function, A, B ∈ B (H) are positive operators, and 0 ≤ α, β ≤ 1. As an application of this operator mean inequality, we present several refinements of the Aujla subadditive inequality for operator monotone decreasing functions. Also, in a similar way, we consider some inequalities of Ando's type. Among other things, it is shown that if Φ is a positive linear map, then