2018/08/25 by Hamid Reza Moradi, Moradi, Hamid Reza, Shigeru Furuichi +3
Mathematics · #47A63 #47A64 #47B15 #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical Inequalities and Applications
paper · pdf · doi:10.48550/arxiv.1808.08342
openalex publication_date 2018/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using the properties of geometric mean, we shall show for any 0≤ α,β≤ 1, f( A∇ αB )≤ f( ( A∇ αB )∇ βA )\sharpαf( ( A∇ αB )∇ βB )≤ f( A )\sharpαf( B ) 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 Φ( A\sharpαB )≤ Φ( ( A\sharpαB )\sharpβA )\sharpαΦ( ( A\sharpαB )\sharpβB )≤ Φ( A )\sharpαΦ( B ).