Speaker
Description
This work aims to introduce a new Buzano-type inequality that integrates and unifies several well-established results from the literature. As a consequence, we present novel numerical radius bounds for operators in semi-Hilbertian spaces. For example, it is proven that
for $T \in \mathcal{L}_{A}(\mathcal{H})$ and a mapping $\chi: [0,1]\subset J \rightarrow [\frac{1}{4},1]$,
\begin{equation}
\omega_{A}^{4}(T) \leqslant \frac{\chi(\lambda)}{4}\left|T^{\sharp_{A}} T+TT^{\sharp_{A}}\right|{A}^{2}+\frac{(1-\chi(\lambda))}{2}\left|T^{\sharp{A}} T+T T^{\sharp_{A}}\right|{A} \omega{A}\left(T^{2}\right).
\end{equation}
Additionally, we establish several bounds for the $\mathbb{A}$-numerical radii of $2 \times 2$ operator matrices. Our results extend and improve certain well-established inequalities from existing literature.