Some new numerical radius and Hilbert-Schmidt numerical radius inequalities for Hilbert space operators. (English) Zbl 07690172
Summary: In this article, we give new upper and lower bounds of numerical radius and Hilbert-Schmidt numerical radius inequalities for Hilbert space operators. In particular, we show that, if \(X\in C^2\) with the Cartesian decomposition \(X = A+iB\), then
\[
\frac{1}{4}\| |X|^2 + |X^\ast|^2\|_2 \leqslant \frac{1}{\sqrt{2}}\omega_2\left(\begin{bmatrix}0 & A^2\\ B^2 & 0\end{bmatrix}\right) \leqslant \omega^2_2(X).
\]
This is an analog of [F. Kittaneh, Stud. Math. 168, No. 1, 73–80 (2005; Zbl 1072.47004)].
MSC:
| 47A12 | Numerical range, numerical radius |
| 47A30 | Norms (inequalities, more than one norm, etc.) of linear operators |
| 47B02 | Operators on Hilbert spaces (general) |
Citations:
Zbl 1072.47004References:
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