Interpolating Numerical Radius Inequalities for Positive Semidefnite Block Matrices

Abstract

In this article, we derive several numerical radius interpolation inequalities related to positive semidefinite block matrices by employing matrix convex function features. In particular, we show that if A,B,C∈M_{n}(C) are such that B is normal and [

A B
B^{∗} C
]≥0, then

w^{2r}(B)≤‖∫₀¹((1-t)(αA^{(r/α)}+(1-α)C^{(r/(1-α))})+tw^{2r}(B)I)²dt‖^{1/2}≤‖αA^{(r/α)}+(1-α)C^{(r/(1-α))}‖

for 0<α<1, r≥1.