A nonlinear Banach–Steinhaus theorem and some meager sets in Banach spaces
Volume 170 / 2005
Studia Mathematica 170 (2005), 303-320
MSC: Primary 46B25, 54E52; Secondary 26A15, 26A24, 26B35, 28A12.
DOI: 10.4064/sm170-3-7
Abstract
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 $L^1(\mu )\times L^1(\mu )$ and $c_0\times c_0$. As another consequence, we get a Banach–Mazurkiewicz type theorem on some residual subset of $C[0,1]$ involving Kharazishvili's notion of ${\mit\Phi} $-derivative.
