Banach–Steinhaus theory revisited: Lineability and spaceability

In this paper we study the divergence behavior of linear approximation processes in general Banach spaces. We are interested in the structure of the set of vectors creating divergence. The Banach–Steinhaus theory gives some information about this set, however, it cannot be used to answer the questio...

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Bibliographic Details
Published in:Journal of approximation theory 2017-01, Vol.213, p.50-69
Main Authors: Boche, Holger, Mönich, Ullrich J.
Format: Article
Language:English
Subjects:
Approximation
Banach spaces
Banach–Steinhaus theorem
Divergence
Lineability
Spaceability
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Summary:In this paper we study the divergence behavior of linear approximation processes in general Banach spaces. We are interested in the structure of the set of vectors creating divergence. The Banach–Steinhaus theory gives some information about this set, however, it cannot be used to answer the question whether this set contains subspaces with linear structure. We give necessary and sufficient conditions for the lineability and the spaceability of the set of vectors creating divergence.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2016.10.002