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

Download

Share

COinS