Factorization in Fréchet spaces
Factorization in some Fréchet algebras of differentiable functions
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.
Factorization of unbounded operators on Köthe spaces
The main result is that the existence of an unbounded continuous linear operator T between Köthe spaces λ(A) and λ(C) which factors through a third Köthe space λ(B) causes the existence of an unbounded continuous quasidiagonal operator from λ(A) into λ(C) factoring through λ(B) as a product of two continuous quasidiagonal operators. This fact is a factorized analogue of the Dragilev theorem [3, 6, 7, 2] about the quasidiagonal characterization of the relation (λ(A),λ(B)) ∈ ℬ (which means that all...
Factorization of weakly compact operators between Banach spaces and Fréchet or (LB)-spaces
Fat equicontinuous groups of homeomorphisms of linear topological spaces and their application to the problem of isometries in linear metric spaces
F-espacios sobre cuerpos locales: La propiedad de extensión.
Finite families of -spaces and multirectangular characteristics.
Finite points of filters in infinite dimensional vector spaces
Finite-dimensional Schauder decompositions in certain Frechet spaces
Fixed-point theory on a Frechet topological vector space.
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 quotients of spaces of real-analytic functions
We characterize all Fréchet quotients of the space (Ω) of (complex-valued) real-analytic functions on an arbitrary open set . We also characterize those Fréchet spaces E such that every short exact sequence of the form 0 → E → X → (Ω) → 0 splits.
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 of Moscatelli type.
Fréchet spaces with a unique unconditional basis
Fréchet spaces with quotients failing the bounded approximation property
Fréchet valued co-echelon spaces
Fréchet-Montel-spaces which are not Schwartz-spaces