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Let B₀(D,ℓ²) denote the space of all upper triangular matrices A such that [Formula: see text] . We also denote by B_0,c(D,ℓ²) the closed Banach subspace of B₀(D,ℓ²) consisting of all upper triangular matrices whose diagonals are compact operators. In this paper we give a duality result between B_0,c(D,ℓ²) and the Bergman–Schatten spaces L_a¹(D,ℓ²). We also give a characterization of the more general Bergman–Schatten spaces L_a^p(D,ℓ²), 1⩽p<∞, in terms of Taylor coefficients, which is similar to that of M. Mateljevic and M. Pavlovic [M. Mateljevic, M. Pavlovic, L^p-behaviour of the integral means of analytic functions, Studia Math. 77 (1984) 219–237] for classical Bergman spaces.