In this article we show that a number of apparently different properties coincide on the set of holomorphic functions on a strict inductive limit (all inductive limits are assumed to be countable and proper) of Banach spaces and that they are all satisfied only in the trivial case of a strict inductive limit of finite dimensional spaces. Thus the linear properties of a strict inductive limit of Banach spaces rarely translate themselves into holomorphic properties.
@article{urn:eudml:doc:44317,
title = {Holomorphic functions on strict inductive limits of Banach spaces.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {5},
year = {1992},
pages = {177-183},
zbl = {0789.46039},
mrnumber = {MR1195077},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44317}
}
Dineen, Seán; Moraes, Luiza A. Holomorphic functions on strict inductive limits of Banach spaces.. Revista Matemática de la Universidad Complutense de Madrid, Tome 5 (1992) pp. 177-183. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44317/