Displaying similar documents to “Compact perturbations of linear differential equations in locally convex spaces”

Factorization of Montel operators

S. Dierolf, P. Domański (1993)

Studia Mathematica

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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. ...

Bounded linear maps between (LF)-spaces.

Angela A. Albanese (2003)

RACSAM

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Characterizations of pairs (E,F) of complete (LF)?spaces such that every continuous linear map from E to F maps a 0?neighbourhood of E into a bounded subset of F are given. The case of sequence (LF)?spaces is also considered. These results are similar to the ones due to D. Vogt in the case E and F are Fréchet spaces. The research continues work of J. Bonet, A. Galbis, S. Önal, T. Terzioglu and D. Vogt.

On convex functions in c(w).

Petr Hájek (1996)

Collectanea Mathematica

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It is proved that no convex and Fréchet differentiable function on c(w), whose derivative is locally uniformly continuous, attains its minimum at a unique point.