Closed Complemented Subspaces of Banach Spaces and Existence of Bounded Quasi-linear Generalized Inverses

被引：2

作者：

Liu Guanqi ^{[1
,3
]}

Hudzik, Henryk ^{[2
]}

Wang Yuwen ^{[1
,3
]}

机构：

[1] Harbin Normal Univ, Yuan Yung Tseng Funct Anal Res Ctr, Harbin 150025, Heilongjiang, Peoples R China

[2] Adam Mickiewicz Univ, Fac Math & Comp Sci, Poznan, Poland

[3] Northeast Normal Univ, Sch Math & Stat, Changchun, Jilin, Peoples R China

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2017年 / 38卷 / 11期

基金：

中国国家自然科学基金;

关键词：

Banach space; bounded quasi-linear (BQL) generalized inverse with respect to projectors; complemented subspace; necessary and sufficient condition; UNIFIED APPROACH; HILBERT-SPACES; OPERATORS; BIFURCATION; SELECTIONS; PROJECTION;

D O I：

10.1080/01630563.2017.1344247

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, an equivalent condition for the existence of a bounded quasi-linear (BQL) generalized inverse of a closed linear operator with respect to projector between two Banach spaces is given. Using the BQL generalized inverse, we give a necessary and sucient condition for a closed linear subspace in a Banach space to be complemented. Finally, an application of the main results to the Saddle-Node bifurcation theorem from multiple eigenvalues in nonlinear analysis is given.

引用

页码：1490 / 1506

页数：17

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