Hahn spaces in Fréchet spaces and applications to real sequence spaces

Abstract

In a joint paper with Grahame Bennett and Toivo Leiger (cf. [3]) the second author introduced for real sequence spaces the Hahn property and the notion of Hahn spaces. The aim of this paper is to extend these notions and a series of results in [3] to subspaces of Fréchet spaces by replacing the space $\omega$ of all real sequences and the set $\chi$ of all sequences of 0's and 1's by any Fréchet space $H$ and a suitable subset $\chi$ of $H$, respectively. Applications of the general considerations to the original case of Hahn spaces of real sequences are also a main subject matter of the paper.