We give another version of the recently developed abstract theory of universal series to exhibit a necessary and sufficient condition of polynomial approximation type for the existence of universal elements. This certainly covers the case of simultaneous approximation with a sequence of continuous linear mappings. In the case of a sequence of unbounded operators the same condition ensures existence and density of universal elements. Several known results, stronger statements or new results can be deduced in a unified way.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm196-2-1,
author = {A. Mouze},
title = {Polynomial approximations and universality},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {103-120},
zbl = {1195.30056},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm196-2-1}
}
A. Mouze. Polynomial approximations and universality. Studia Mathematica, Tome 196 (2010) pp. 103-120. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm196-2-1/