Geodesic
Factorization of Montel operators
Studia Mathematica, Tome 107 (1993) no. 1, pp. 15-32

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-107-1-15-32
Keywords: Fréchet space, Fréchet-Montel space, complete LB-space, Montel LB-space, regular LB-space, Mackey completion of an LB-space, bornologicity of C(K, E)

S. Dierolf 1

1 
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S. Dierolf. Factorization of Montel operators. Studia Mathematica, Tome 107 (1993) no. 1, pp. 15-32. doi: 10.4064/sm-107-1-15-32

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