A nonlinear Banach–Steinhaus theorem and some meager sets in Banach spaces

Tom 170 / 2005

Jacek Jachymski Studia Mathematica 170 (2005), 303-320 MSC: Primary 46B25, 54E52; Secondary 26A15, 26A24, 26B35, 28A12. DOI: 10.4064/sm170-3-7

Streszczenie

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.

Autorzy

  • Jacek JachymskiInstitute of Mathematics
    Technical University of Łódź
    Żwirki 36
    90-924 Łódź, Poland
    e-mail

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