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Let B 0 (D, 2 ) denote the space of all upper triangular matrices A such that lim r→1 − (1 − r 2 ) (A * C (r)) B( 2 ) = 0. We also denote by B 0,c (D, 2 ) the closed Banach subspace of B 0 (D, 2 ) consisting of all upper triangular matrices whose diagonals are compact operators. In this paper we give a duality result between B 0,c (D, 2 ) and the Bergman-Schatten spaces L 1 a (D, 2 ). We also give a characterization of the more general Bergman-Schatten spaces L p a (D, 2 ), 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.

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