OICC Press Mathematical Analysis and its Contemporary Applications 2 1 2020 03 20 Toeplitzness of weighted composition operators 10.30495/maca.2020.679850 EN Massoud Salehi Sarvestani Department of Mathematics, Savadkoh Branch, Islamic Azad University, Savadkoh, Iran. Journal Article 2020 03 20 For a bounded analytic map ψ on the unit disk D and analytic self-map φ of D, a weighted composition operator Cψ,φ on the Hardy space H² = H²(D) is defined by Cψ,φ f = ψ·f∘φ. In this paper, we study the asymptotically Toeplitzness of weighted composition operators and their adjoints in different topology on B(H²).