Document Type
Article
Publication Date
4-1-2017
Abstract
It is well known, as follows from the Banach-Steinhaus theorem, that if a sequence {yn}n=1∞ of linear continuous functionals in a Fréchet space converges pointwise to a linear functional Y, Y(x) = lim n → ∞〈yn, x〉 for all x, then Y is actually continuous. In this article, we prove that in a Fréchet space the continuity of Y still holds if Y is the finite part of the limit of 〈yn, x〉 as n→ ∞. We also show that the continuity of finite part limits holds for other classes of topological vector spaces, such as LF-spaces, DFS-spaces, and DFS∗-spaces and give examples where it does not hold.
Publication Source (Journal or Book title)
Bulletin of the Malaysian Mathematical Sciences Society
First Page
907
Last Page
918
Recommended Citation
Estrada, R., & Vindas, J. (2017). A Generalization of the Banach-Steinhaus Theorem for Finite Part Limits. Bulletin of the Malaysian Mathematical Sciences Society, 40 (2), 907-918. https://doi.org/10.1007/s40840-017-0450-7
