Factorization of Montel operators

Tom 107 / 1993

S. Dierolf Studia Mathematica 107 (1993), 15-32 DOI: 10.4064/sm-107-1-15-32

Streszczenie

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.

Autorzy

  • S. Dierolf

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