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