In this paper we generalize the well-known result which says that the composition of quasi-nuclear maps is nuclear. More precisely, we define what we call a 2-quasi-l -nuclear map between normed spaces, and we prove that the composition of a 2-quasi-l -nuclear map with a quasi- l -nuclear map is a pseudo-l -nuclear map. Also, we prove that a quasi-l -nuclear map is a 2-quasi-l -nuclear map. For a nuclear G\infty -space, we prove that a linear map T between normed spaces is 2-quasi-l -nuclear if and only if it is quasi-l -nuclear

In this paper we generalize the well-known result which says that the composition of quasi-nuclear maps is nuclear. More precisely, we define what we call a 2-quasi-l -nuclear map between normed spaces, and we prove that the composition of a 2-quasi-l -nuclear map with a quasi- l -nuclear map is a pseudo-l -nuclear map. Also, we prove that a quasi-l -nuclear map is a 2-quasi-l -nuclear map. For a nuclear G\infty -space, we prove that a linear map T between normed spaces is 2-quasi-l -nuclear if and only if it is quasi-l -nuclear