Open AccessBanach-Steinhaus Theorem for the Space P of All Primitives of Henstock-Kurzweil Integrable Functions
Author(s) -
Wan Sing Ng
Publication year - 2021
Publication title -
new zealand journal of mathematics
Language(s) - English
Resource type - Journals
eISSN - 1179-4984
pISSN - 1171-6096
DOI - 10.53733/114
Subject(s) - mathematics , banach space , eberlein–šmulian theorem , pure mathematics , bounded inverse theorem , norm (philosophy) , closed graph theorem , bounded function , integrable system , representation theorem , picard–lindelöf theorem , square integrable function , discrete mathematics , mathematical analysis , danskin's theorem , fixed point theorem , lp space , finite rank operator , political science , law
In this paper, it is shown how the Banach-Steinhaus theorem for the space P of all primitives of Henstock-Kurzweil integrable functions on a closed bounded interval, equipped with the uniform norm, can follow from the Banach-Steinhaus theorem for the Denjoy space by applying the classical Hahn-Banach theorem and Riesz representation theorem.