Factorization of compact operators and finite representability of Banach spaces with applications to Schwartz spaces
Factorization of Montel operators
Consider the following conditions. (a) Every regular LB-space is complete; (b) if an operator T between complete LB-spaces maps bounded sets into relatively compact sets, then T factorizes through a Montel LB-space; (c) for every complete LB-space E the space C (βℕ, E) is bornological. We show that (a) ⇒ (b) ⇒ (c). Moreover, we show that if E is Montel, then (c) holds. An example of an LB-space E with a strictly increasing transfinite sequence of its Mackey derivatives is given.
Finite points of filters in infinite dimensional vector spaces
Formal extension of the Whitney functor and duality
Formes et coformes sur un espace nucléaire complet
Fréchet interpolation spaces and Grothendieck operator ideals.
Starting with a continuous injection I: X → Y between Banach spaces, we are interested in the Fréchet (non Banach) space obtained as the reduced projective limit of the real interpolation spaces. We study relationships among the pertenence of I to an operator ideal and the pertenence of the given interpolation space to the Grothendieck class generated by that ideal.
Fréchet Schwartz spaces and approximation properties.
Fréchet spaces of Moscatelli type.
Fréchet-Montel-spaces which are not Schwartz-spaces