On different types of non-distinguished Fréchet spaces

Abstract

In this paper,we investigate new examples of non-distinguished Fréchet spaces and determine their type of non-distinguishedness in the above sense. We first concentrate on the so-called spaces of «Moscatelli-type».In a second part, we consider sequence spaces and function spaces and, among other things, classify the examples previously given by Bonet and Taskinen [7]. Although we mainly concentrate here in the presentation and analysis of examples, we also expect that our study provides a better understanding of non-distinguished Fréchet spaces.