ELB holomorphic factorization over projective limit representations
Entire functions on nuclear sequence spaces.
Espaces collectivement localement convexes
Espaces du type Sobolev sur un espace de Hilbert complexe
Example of a sequentially incomplete regular inductive limit of Banach spaces.
Examples on Projective Spectra of (LB)-spaces.
Extension maps in ultradifferentiable and ultraholomorphic function spaces
The problem of the existence of extension maps from 0 to ℝ in the setting of the classical ultradifferentiable function spaces has been solved by Petzsche [9] by proving a generalization of the Borel and Mityagin theorems for -spaces. We get a Ritt type improvement, i.e. from 0 to sectors of the Riemann surface of the function log for spaces of ultraholomorphic functions, by first establishing a generalization to some nonclassical ultradifferentiable function spaces.
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
(F)-Spaces and Strict (LF)-Spaces.
Generalized Hermitean ultradistributions
In this paper we define, by duality methods, a space of ultradistributions . This space contains all tempered distributions and is closed under derivatives, complex translations and Fourier transform. Moreover, it contains some multipole series and all entire functions of order less than two. The method used to construct led us to a detailed study, presented at the beginning of the paper, of the duals of infinite dimensional locally convex spaces that are inductive limits of finite dimensional...
Generalized precompactness and mixed topologies.
The equicontinuous sets of locally convex generalized inducted limit (or mixed) topologies are characterized as generalized precompact sets. Uniformly pre-Lebesgue and Lebesgue topologies in normed Riesz spaces are investigated and it is shown that order precompactness and mixed topologies can be used to great advantage in the study of these topologies.
Geometry of nuclear spaces - I