A SURJECTIVE SUMMATION OPERATOR WITH NO LIPSCHITZ RIGHT INVERSE

被引：0
|
作者：
Laustsen, Niels Jakob [1 ]
Messerschmidt, Miek [2 ]
Wortel, Marten [2 ]
机构：
[1] Univ Lancaster, Fylde Coll, Dept Math & Stat, Lancaster LA1 4YF, England
[2] Univ Pretoria, Dept Math & Appl Math, ZA-0028 Pretoria, South Africa
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2024年 / 152卷 / 01期
基金：
芬兰科学院; 新加坡国家研究基金会;
关键词：
Banach space; summation operator; surjection; right inverse; Lipschitz; OPEN MAPPING-THEOREM;
D O I：
10.1090/proc/16496
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that there exists a Banach space X which contains closed subspaces Y and Z with Y + Z = X such that the associated surjective sum-mation operator Sigma: Y x Z -> X defined by Sigma(y, z) = y + z for y is an element of Y and z is an element of Z has no Lipschitz right inverse.
引用
收藏
页码：253 / 266
页数：14
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