Geodesic
Polynomial approximations and universality
A. Mouze1
1 Laboratoire Paul Painlevé, UMR 8524 and École Centrale de Lille Cité Scientifique 59650 Villeneuve d'Ascq, France
Studia Mathematica, Tome 196 (2010) no. 2, pp. 103-120 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm196-2-1
Keywords: another version recently developed abstract theory universal series exhibit necessary sufficient condition polynomial approximation type existence universal elements certainly covers simultaneous approximation sequence continuous linear mappings sequence unbounded operators condition ensures existence density universal elements several known results stronger statements results deduced unified

A. Mouze 1

1 Laboratoire Paul Painlevé, UMR 8524 and École Centrale de Lille Cité Scientifique 59650 Villeneuve d'Ascq, France 
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A. Mouze. Polynomial approximations and universality. Studia Mathematica, Tome 196 (2010) no. 2, pp. 103-120. doi: 10.4064/sm196-2-1

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