Polynomial approximations and universality
Tom 196 / 2010
Studia Mathematica 196 (2010), 103-120
MSC: 30B30, 30E10, 30K05, 30K10, 41A65, 47B37.
DOI: 10.4064/sm196-2-1
Streszczenie
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.
