Some $${\mathbb {A}}$$-numerical radius inequalities for $$d\times d$$ operator matrices

Let A be a positive (semidefinite) bounded linear operator acting on complex Hilbert space \(\big ({\mathcal {H}}, \langle \cdot , \rangle \big )\). The semi-inner product \({\langle x, y\rangle }_A := Ax, \), \(x, y\in {\mathcal {H}}\) induces seminorm \({\Vert \Vert }_A\) \({\mathcal {H}}\). T an A-bounded {H}}\), the A-numerical radius of is given by $$\begin{aligned} \omega _A(T) = \sup \Big \{\big |{\langle Tx, x\rangle }_A\big |\;; \,\,x\in \;{\Vert x\Vert 1\Big \}. \end{aligned}$$In this paper, we establish several inequalities for \(\omega _{\mathbb {A}}({\mathbb {T}})\), where \({\mathbb {T}}=(T_{ij})\) \(d\times d\) matrix with \(T_{ij}\) are operators and {A}}\) diagonal whose each entry A. Some obtained results generalize some earlier proved Bhunia et al. (Math. Inequal. Appl. 24(1), 167–183, 2021).