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
Formes et coformes sur un espace nucléaire complet
Fréchet Schwartz spaces and approximation properties.
Fréchet spaces of continuous vector-valued functions: Complementability in dual Fréchet spaces and injectivity
Fréchet spaces of strongly, weakly and weak*-continuous Fréchet space valued functions are considered. Complete solutions are given to the problems of their injectivity or embeddability as complemented subspaces in dual Fréchet spaces.
Fréchet spaces with a unique unconditional basis
Fréchet-Montel-spaces which are not Schwartz-spaces