Some operator mean inequalities for sector matrices

In this article, we obtain some operator mean inequalities of sectorial matrices involving operator monotone functions. Among other results, it is shown that if A, B is an element of M-n (C) are such that W (A), W (B) subset of S-alpha, f, g, h is an element of m are such that g'(1) = h'(1) = t for some t is an element of (0, 1) and 0 < mI(n) <= RA, RB <= MIn, then R(Phi(f(A))sigma(h)Phi(f(B))) <= sec(4)(alpha)KR Phi(f(A sigma B-g)), where M, m are scalars and m is the collection of all operator monotone function phi : (0, infinity) -> (0, infinity) satisfying phi(1) = 1. Moreover, we refine a norm inequality of sectorial matrices involving positive linear maps, which is a result of Bedrani, Kittaneh and Sababheh.

Automated summary

This article presents operator mean inequalities of sectorial matrices involving operator monotone functions and refines a norm inequality of sectorial matrices involving positive linear maps. The results also include discussions on specific mathematical conditions and criteria.