Inequalities for operator space numerical radius of 2 × 2 block matrices
Mohammad Sal Moslehian, Mostafa Sattari · Journal of Mathematical Physics · 2015
In this paper, we study the relationship between operator space norm and operator space numerical radius on the matrix space Mn(X), when X is a numerical radius operator space. Moreover, we establish several inequalities for operator space numerical radius and the maximal numerical radius norm of 2 × 2 operator matrices and their off-diagonal parts. One of our main results states that if (X, (On)) is an operator space, then 12max(Wmax(x1+x2),Wmax(x1−x2))≤Wmax(0x1x20)≤12Wmax(x1+x2)+Wmax(x1−x2) for all x1,x2∈Mn(X).