A bornological approach to rotundity and smoothness applied to approximation.
A Class of Bornological Barrelled Spaces which Are not Ultrabornological.
A normability condition on locally convex spaces.
In a previous work (1990) we introduced a certain property (y) on locally convex spaces and used it to remove the assumption of separability from the theorem of Bellenot and Dubinsky on the existence of nuclear Köthe quotients of Fréchet spaces. Our purpose is to examine condition (y) further and relate it to some other normability conditions. Some of our results were already announced in Önal (1989).
A note on closed graph theorems.
A useful algebra for functional calculus
We show that some unital complex commutative LF-algebra of -tempered functions on (M. Hemdaoui, 2017) equipped with its natural convex vector bornology is useful for functional calculus.
Axioms for convenient calculus
Banach-Mackey, locally complete spaces, and -summability.
Banach-Mackey spaces.
Barreledness of subspaces of countable codimension and the closed graph theorem
Caractérisations des b-espaces libres.
Compatible topologies and bornologies on modules
Compatible topologies and bornologies on modules are introduced and studied.
Convolution operators in infinite dimension.
Corrigendum: Mackey convergence and quasi-sequentially webbed spaces.
Countably determined locally convex spaces
Equivariant local cyclic homology and the equivariant Chern-Connes character.
Espaces vectoriels bornologiques ordonnés
Espacios Lα e integración bornológica.
Examples of convex functions and classifications of normed 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.
Fragmentability of the Dual of a Banach Space with Smooth Bump
We prove that if a Banach space X admits a Lipschitz β-smooth bump function, then (X ∗ , weak ∗ ) is fragmented by a metric, generating a topology, which is stronger than the τβ -topology. We also use this to prove that if X ∗ admits a Lipschitz Gateaux-smooth bump function, then X is sigma-fragmentable.