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.
@article{bwmeta1.element.bwnjournal-article-smv107i1p15bwm, author = {S. Dierolf and P. Doma\'nski}, title = {Factorization of Montel operators}, journal = {Studia Mathematica}, volume = {104}, year = {1993}, pages = {15-32}, zbl = {0810.46002}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv107i1p15bwm} }
Dierolf, S.; Domański, P. Factorization of Montel operators. Studia Mathematica, Tome 104 (1993) pp. 15-32. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv107i1p15bwm/
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