Let U be an open subset of a separable Banach space. Let ℱ be the collection of all holomorphic mappings f from the open unit disc 𝔻 ⊂ ℂ into U such that f(𝔻) is dense in U. We prove the lineability and density of ℱ in appropriate spaces for different choices of U.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm210-2-5,
author = {Jer\'onimo L\'opez-Salazar},
title = {Lineability of the set of holomorphic mappings with dense range},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {177-188},
zbl = {1273.46031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm210-2-5}
}
Jerónimo López-Salazar. Lineability of the set of holomorphic mappings with dense range. Studia Mathematica, Tome 209 (2012) pp. 177-188. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm210-2-5/