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A normability condition on locally convex spaces.

S. Önal, T. Terzioglu (1991)

Revista Matemática de la Universidad Complutense de Madrid

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).

Banach-Mackey spaces.

Qiu, Jing Hui, McKennon, Kelly (1991)

International Journal of Mathematics and Mathematical Sciences

Factorization of Montel operators

S. Dierolf, P. Domański (1993)

Studia Mathematica

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

Kortezov, I. (1998)

Serdica Mathematical Journal

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.

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