On 2-λ-Nuclearity Maps

Abstract

In this paper we give an answer for the following problem: Is 2-quasi-λ(P)-nuclear maps between normed spaces equivalent to quasi-λ(P)-nuclear maps for a non nuclear G_∞-space λ(P)? [3]. Also, we define the k-K¨othe space λ^(k), and we prove that if λ^(k) is generated from power sets of infinite type P₁, P₂, ... , P_k and λ^(k) is nuclear, then 2-quasi-λ^(k)-nuclear maps between normed spaces is equivalent to quasi-λ^(k)-nuclear maps.

Key words and phrases. Nuclear maps, Smooth sequence spaces, Nuclearity, quasi-λ-nuclear map.

2000 Mathematics Subject Classification. Primary: 46A45, Secondary: 47B10