z-logo
open-access-imgOpen Access
Banach-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.   

The content you want is available to Zendy users.

Already have an account? Click here to sign in.
Having issues? You can contact us here