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\begin{document}$$\mathcal {H}$$\end{document} be a complex Hilbert space and let A be a positive operator on H\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {H}$$\end{document}. We obtain new bounds for the A-numerical radius of operators in semi-Hilbertian space BA(H)\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {B}_A(\mathcal {H})$$\end{document} that generalize and improve on the existing ones. Further, we estimate an upper bound for the A\documentclass[12pt]{minimal}
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\begin{document}$$\mathbb {A}$$\end{document}-operator seminorm of 2×2\documentclass[12pt]{minimal}
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\begin{document}$$2\times 2$$\end{document} operator matrices, where A=diag(A,A)\documentclass[12pt]{minimal}
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\begin{document}$$\mathbb {A}=\text{ diag }(A,A)$$\end{document}. The bound obtained here generalizes the earlier related bound.
