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

被引：12

作者：

Jachymski, J ^{[1
]}

机构：

[1] Tech Univ Lodz, Inst Math, PL-90924 Lodz, Poland

来源：

STUDIA MATHEMATICA | 2005年 / 170卷 / 03期

关键词：

Banach-Steinhaus theorem; Baire category; subadditivity; semicontinuity; sigma-finite measure; integrable function; Phi-derivative;

D O I：

10.4064/sm170-3-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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) x L-1 (mu) and c(0) x 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 Phi-derivative.

引用

页码：303 / 320

页数：18