Banach-Steinhaus theory revisited: Lineability and spaceability
نویسندگان
چکیده
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 divergence creating functions. 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 divergence creating functions.
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عنوان ژورنال:
- Journal of Approximation Theory
دوره 213 شماره
صفحات -
تاریخ انتشار 2017