Abstract
In this paper we give an answer for the following problem: Is 2-quasi, lambda(P)-nuclear maps between normed spaces equivalent to quasi-lambda(P)-nuclear maps for a non nuclear G(infinity)-space lambda(P)? [3]. Also, we define the k-K "othe space lambda((k)), and we prove that if lambda((k)) is generated from power sets of infinite type P 1; P 2,...; P k and lambda((k)) is nuclear, then 2-quasi-lambda((k))-nuclear maps between normed spaces is equivalent to quasi-lambda((k))-nuclear maps.