Open AccessBanach-Steinhaus Theorem for the Space P of All Primitives of Henstock-Kurzweil Integrable Functions
Author(s) -
Wee Leng 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.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom