On Power Series Subspaces of Certain Nuclear Fréchet Spaces

Abstract

Abstract. The diametral dimension, (E), and the approximate diametral dimension, (E) of an element E of a large class of nuclear Fréchet spaces are set theoretically between the corresponding invariant of power series spaces 1(") and 1(") for some exponent sequence ". Aytuna et al., [2], proved that E contains a complemented subspace which is isomorphic to 1(") provided (E) = ( 1(")) and " is stable. In this article, we will consider the other extreme case and we proved that in this large family, there exist nuclear Fréchet spaces, even regular nuclear Köthe spaces, satisfying (E) = ( 1(")) such that there is no subspace of E which is isomorphic to 1(").