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Factorization of Montel operators

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Dierolf S., Domański P.

Studia Mathematica

1993

tom 107

nr 1

15-32

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.

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1 Studia Mathematica

1 Dierolf S.

1 Domański P.

1 1993

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Factorization of Montel operators