More inequalities on numerical radii of sectorial matrices

In this article, we refine some numerical radius inequalities of sectorial matrices recently obtained by Bedrani, Kittaneh and Sababheh. Among other results, it is shown that if A(i) is an element of M-n(C) with W(A(i)) subset of S-alpha, i = 1, 2 ..., n, and a(1), ..., a(n) are positive real numbers with Sigma(n)(j=1) a(j) = 1, then omega(t)(Sigma(n)(i=1) a(i)A(i)) <= cos(2t)(alpha)omega(Sigma(n)(i=1) a(i)A(i)(t)), where t is an element of [-1, 0]. An improvement of the Heinz-type inequality for the numerical radii of sectorial matrices is also given. Moreover, we present some numerical radius inequalities of sectorial matrices involving positive linear maps.

Automated summary

This article refines some numerical radius inequalities of sectorial matrices obtained by Bedrani, Kittaneh, and Sababheh, as well as presents new inequalities involving positive linear maps.