Let B0 (D, ℓ2) denote the space of all upper triangular matrices A such that limr → 1- (1 - r2) {norm of matrix} (A * C (r))′ {norm of matrix}B (ℓ2) = 0. We also denote by B0, 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 B0, c (D, ℓ2) and the Bergman-Schatten spaces La1 (D, ℓ2). We also give a characterization of the more general Bergman-Schatten spaces Lap (D, ℓ2), 1 ≤ p < ∞, in terms of Taylor coefficients, which is similar to that of M. Mateljevic and M. Pavlovic [M. Mateljevic, M. Pavlovic, Lp-behaviour of the integral means of analytic functions, Studia Math. 77 (1984) 219-237] for classical Bergman spaces.