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.
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. ...
Sunday Gluyemi (1997)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Stanislav Tomášek (1970)
Commentationes Mathematicae Universitatis Carolinae
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Kučera, Jan (1999)
International Journal of Mathematics and Mathematical Sciences
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Wim H. Schikhof (1984-1985)
Groupe de travail d'analyse ultramétrique
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Carlos Bosch, Jan Kučera (2002)
Czechoslovak Mathematical Journal
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Any inductive limit of bornivorously webbed spaces is sequentially complete iff it is regular.
José Bonet, Susanne Dierolf, Carmen Fernández (1989)
Publicacions Matemàtiques
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Let L be a normal Banach sequence space such that every element in L is the limit of its sections and let E = ind E be a separated inductive limit of the locally convex spaces. Then ind L(E) is a topological subspace of L(E).