Some inequalities involving Hilbert-Schmidt numerical radius on 2 × 2 operator matrices


Monire Hajmohamadi, Rahmatollah Lashkaripour




We present some inequalities related to the Hilbert-Schmidt numerical radius of 2 × 2 operator matrices. More precisely, we present a formula for the Hilbert-Schmidt numerical radius of an operator as follows: w 2 (T) = sup α 2 +β 2 =1 αA + βB 2 , where T = A + iB is the Cartesian decomposition of T ∈ HS(H)