Multiplication in the space of functions of bounded variation

被引：1

作者：

Kowalczyk, Stanislaw ^{[1
]}

Turowska, Malgorzata ^{[1
]}

机构：

[1] Pomeranian Univ Slupsk, Inst Math, Ul Kozietulskiego 6-7, PL-76200 Slupsk, Poland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 472卷 / 01期

关键词：

Bilinear operation; Open mapping; Uniformly open mapping; Space of functions of bounded variation; Multiplication in function spaces; C(X);

D O I：

10.1016/j.jmaa.2018.11.045

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let BV[0, 1] denote the Banach space of all functions on the unit interval that have bounded variation. When endowed with the pointwise product, BV[0, 1] becomes a Banach algebra. We will demonstrate that multiplication in BV[0, 1] is an open map. Using an observation of F. Nazarov (who has kindly permitted us to include it), we show that multiplication is not uniformly open and we thereby solve in the negative the problem of whether open bilinear maps are automatically uniformly open. (C) 2018 Published by Elsevier Inc.

引用

页码：696 / 704

页数：9

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