A new characterization of Bergman–Schatten spaces and a duality result

Let B0(D,ℓ2) denote the space of all upper triangular matrices A such that limr→1−(1−r2)‖(A∗C′(r))‖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 . We also give a characterization of the more general Bergman–Schatten spaces , 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.