# Factorization of Montel operators

Studia Mathematica (1993)

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

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topDierolf, 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 -

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