# Factorization of Montel operators

Studia Mathematica (1993)

• Volume: 107, Issue: 1, page 15-32
• ISSN: 0039-3223

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## Abstract

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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.

## How to cite

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Dierolf, S., and Domański, P.. "Factorization of Montel operators." Studia Mathematica 107.1 (1993): 15-32. <http://eudml.org/doc/216019>.

@article{Dierolf1993,
abstract = {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.},
author = {Dierolf, S., Domański, P.},
journal = {Studia Mathematica},
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); Mackey derivatives},
language = {eng},
number = {1},
pages = {15-32},
title = {Factorization of Montel operators},
url = {http://eudml.org/doc/216019},
volume = {107},
year = {1993},
}

TY - JOUR
AU - Dierolf, S.
AU - Domański, P.
TI - Factorization of Montel operators
JO - Studia Mathematica
PY - 1993
VL - 107
IS - 1
SP - 15
EP - 32
AB - 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.
LA - eng
KW - 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); Mackey derivatives
UR - http://eudml.org/doc/216019
ER -

## References

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