Central limit theorem for linear processes with values in a Hilbert space

In this paper we study the behavior of Sn = ∑nk = 1αnkεk associated to an i.i.d. sequence (εk, k ∈ Z) with values in a real separable Hilbert space H of infinite dimension, and where (αnk, 1 ⩽ k ⩽ n) is a triangular array of bounded linear operators from H to H. We shall provide sufficient conditions for the CLT for (Sn, n ⩾ 1) imposed on the norm of the operators and on the moments of Sn.