Hilbert-Schmidt numerical radius inequalities for \(2\times 2\) operator matrices. (English) Zbl 1489.47025
Summary: Let \(A\) and \(C\) be operators in the Hilbert-Schmidt class. Then \[\max(\sqrt{2}w_2(A),\sqrt{2}w_2(C))\le w_2\left(\begin{bmatrix}A & C \\ -C & -A\end{bmatrix}\right)\le\sqrt{2}(w_2(A)+w_2(C)).\] Several Hilbert-Schmidt numerical radius inequalities are given.
MSC:
| 47A63 | Linear operator inequalities |
| 47A12 | Numerical range, numerical radius |
| 47B02 | Operators on Hilbert spaces (general) |
| 47B15 | Hermitian and normal operators (spectral measures, functional calculus, etc.) |
