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Displaying similar documents to “Spaces C(X) and L(μ) as direct or inverse limits in the category of Banach spaces”

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

Jacek Jachymski (2005)

Studia Mathematica

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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 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.