
Journal of Convex Analysis 31 (2024), No. 1, 227242 Copyright Heldermann Verlag 2024 ANumerical Radius of SemiHilbert Space Operators Messaoud Guesba Dept. of Mathematics, Faculty of Exact Sciences, El Oued University, Algeria guesbamessaoud@univeloued.dz Pintu Bhunia Dept. of Mathematics, Indian Institute of Science, Bengaluru, Karnataka, India pintubhunia5206@gmail.com Kallol Paul Dept. of Mathematics, Jadavpur University, Kolkata, West Bengal, India kalloldada@gmail.com [Abstractpdf] Let $\mathbf{A=}\left(\!\! \begin{array}{cc} A & 0 \\ 0 & A \end{array}\!\! \right)$ be a $2\times 2$ diagonal operator matrix whose each diagonal entry is a positive bounded linear operator $A$ acting on a complex Hilbert space ${\mathcal{H}}$. Let $T,S$ and $R$ be bounded linear operators on ${\mathcal{H}}$ admitting $A$adjoints, where $T$ and $R$ are $A$positive. By considering an $\mathbf{A}$positive $2 \times 2$ operator matrix $\left(\!\!\begin{array}{cc}T & S^{^{\sharp _{A}}} \\S & R \end{array}\!\!\right)$, we develop several upper bounds for the $A$numerical radius of $S$. Applying these upper bounds we obtain new $A$numerical radius bounds for the product and the sum of arbitrary operators which admit $A$adjoints. Related other inequalities are also derived. Keywords: Anumerical radius, positive operator, seminorm, semiinner product. MSC: 47A05, 47A12, 47A30, 47B15. [ Fulltextpdf (130 KB)] for subscribers only. 