We establish a Banach-Steinhaus type theorem for nonlinear functionals of several variables. As an application, we obtain extensions of the recent results of Balcerzak and Wachowicz on some meager subsets of L¹(μ) × L¹(μ) and c₀ × c₀. As another consequence, we get a Banach-Mazurkiewicz type theorem on some residual subset of C[0,1] involving Kharazishvili's notion of Φ-derivative.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-3-7,
author = {Jacek Jachymski},
title = {A nonlinear Banach-Steinhaus theorem and some meager sets in Banach spaces},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {303-320},
zbl = {1090.46015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-3-7}
}
Jacek Jachymski. A nonlinear Banach-Steinhaus theorem and some meager sets in Banach spaces. Studia Mathematica, Tome 166 (2005) pp. 303-320. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-3-7/