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

• Autorzy: Jacek Jachymski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54E52: Baire category, Baire spaces
• 26B35: Special properties of functions of several variables, H\"older conditions, etc.
• 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems
• 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)
• 28A12: Contents, measures, outer measures, capacities
• 46B25: Classical Banach spaces in the general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 170
• Numer: 3
• Strony: 303-320

Daty

wydano

2005

Twórcy

autor

Jacek Jachymski

• Institute of Mathematics, Technical University of Łódź, Żwirki 36, 90-924 Łódź, Poland

Identyfikatory

DOI

10.4064/sm170-3-7