Geodesic
A nonlinear Banach–Steinhaus theorem and some meager sets in Banach spaces
Jacek Jachymski1
1 Institute of Mathematics Technical University of Łódź Żwirki 36 90-924 Łódź, Poland
Studia Mathematica, Tome 170 (2005) no. 3, pp. 303-320 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm170-3-7
Keywords: establish banach steinhaus type theorem nonlinear functionals several variables application obtain extensions recent results balcerzak wachowicz meager subsets times times another consequence get banach mazurkiewicz type theorem residual subset involving kharazishvilis notion mit phi derivative

Jacek Jachymski 1

1 Institute of Mathematics Technical University of Łódź Żwirki 36 90-924 Łódź, Poland 
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 some meager sets in {Banach} spaces},
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 some meager sets in Banach spaces
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 some meager sets in Banach spaces
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Jacek Jachymski. A nonlinear Banach–Steinhaus theorem and
 some meager sets in Banach spaces. Studia Mathematica, Tome 170 (2005) no. 3, pp. 303-320. doi: 10.4064/sm170-3-7

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