Generalizations of numerical radius inequalities related to block matrices


Aliaa Burqan, Ahmad Abu-Rahma




We establish several numerical radius inequalities related to 2×2 positive semidefinite block matrices. It is shown that if A,B,C ∈Mn(C) are such that [ A B∗ B C ] ≥ 0, then wr(B) ≤ 1 2 ‖Ar + Cr‖ , for r ≥ 1. Related numerical radius inequalities for sums and products of matrices are also given