Matrix transformation and statistical convergence

In this paper we will say that a sequence x(k) is lambda A-statistically convergent, if for every epsilon > 0, lim(n ->infinity) 1/lambda(n) vertical bar{k epsilon I-n : vertical bar[AX](k) - L vertical bar >= }vertical bar = 0 with l(n) = [n - lambda(n) + 1, n], where A is an infinite matrix and lambda a strictly increasing sequence of positive numbers tending to infinity such that lambda(1) = 1 and lambda(n+1) <= lambda(n) + 1 for all n. Using the Banach algebra (w(0)(lambda), w(0)(lambda)) we get sufficient conditions to have a sequence lambda, A(-1)-statistically convergent. Then we deduce conditions for a sequence to be lambda, (N) over bar (q)-statistically convergent. Finally we get results in the cases when A is the operator C (mu) and the Cesaro operator. (c) 2006 Elsevier Inc. All rights reserved.