2-quasi-$lambda$-nuclear maps

Abstract

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-$lambda$ -nuclear map between normed spaces, and we prove that the composition of a 2-quasi-$lambda$ -nuclear map with a quasi- $lambda$ -nuclear map is a pseudo-$lambda$ -nuclear map. Also, we prove that a quasi-$lambda$ -nuclear map is a 2-quasi-$lambda$ -nuclear map. For a nuclear $G_{infty}$ -space, we prove that a linear map T between normed spaces is 2-quasi-$lambda$ -nuclear if and only if it is quasi-$lambda$ -nuclear