Power series spaces ?(?) and associated ?(?)-nuclearity

Abstract

The class of strongly nuclear spaces was introduced by Martineau [8] and also rediscovered by Brudovskii [1, 2]. The definition of strongly nuclear maps is related to the space s of rapidly decreasing sequences (see [9]). In this paper we introduce the class of A(e)-nuclear maps, where A(e) is a ~enerat power series space, known to include as special cases the familiar spaces s and F, the space of entire functions (see [3]). We define then the notion of A(c0nuclear spaces and obtain a criterion for the A (e)-nuclearity of sequence spaces 2(P). K6the [7] has proved such a criterion for the s-nuclearity of 2(P). Some applications of this criterion are given and finally we obtain a product of several copies of [A(e)]; as a universal A(e)-nuclear space.