On Numerical Radius Inequalities for Operator Matrices. (18th August 2019) - Guelfen, Hanane; Kittaneh, Fuad
Abstract: The aim of this article is to prove several new numerical radius inequalities for n × n operator matrices on a Hilbert space. Let H 1, H 2, …, H n be complex Hilbert spaces, and let T = [ T i j ] be an n × n operator matrix with T i j ∈ B ( H j, H i ) . Among other inequalities, it shown that ω ( T ) ≤ 1 2 ∑ i = 1 n ( w ( T i i ) + ω 2 ( T i i ) + ∑ j = 1 j ≠ i n | | T i j | | 2 ), where ω ( · ) and | | · | | denote the numerical radius and the usual operator norm, respectively.