Fréchet Spaces without continuous Norms and without Bases

On twisted Fréchet and (LB)-spaces

“…Twisted spaces were introduced by the second author (in [16]) to answer a question about the structure of Fréchet spaces without a continuous norm; since then, they have been useful in many constructions involving Fréchet spaces as well as their duals in a variety of contexts. These constructions were used extensively (cf.…”

“…In particular, a modification of the method of [ 16] allows us to build nonreflexive twisted Fréchet spaces and to give examples of twisted spaces with nontwisted duals. The same example shows that a twisted Fréchet space and a countable product of Banach spaces can have the same dual.…”

Montel subspaces of Fréchet spaces of Moscatelli type

“…To do this, we first study the topology induced by E on its Montel subspaces, extending a result on Fr6chet-Montel spaces of Moscatelli type in [4].We recall that the Frechet spaces of Moscatelli type were introduced and studied by J. Bonet and S. Dierolf in [4]; the general idea behind the construction of such spaces was due to V. B. Moscatelli [7].The paper has three sections. The first one is devoted to the necessary definitions and preliminaries; in the second we prove our main result and in the third we apply it to some concrete function spaces of Frechet-Sobolev type.…”

“…For more about such spaces the reader is referred to, for example, [4] and [7]. Also, we introduce for every n e N the following continuous maps…”

“…We recall that the Frechet spaces of Moscatelli type were introduced and studied by J. Bonet and S. Dierolf in [4]; the general idea behind the construction of such spaces was due to V. B. Moscatelli [7].…”