Closed Complemented Subspaces of Banach Spaces and Existence of Bounded Quasi-linear Generalized Inverses. (2nd November 2017)

• Record Type: Journal Article
• Authors: Guanqi, Liu; Hudzik, Henryk; Yuwen, Wang
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 11(2017)
• Page Start: 1490
• Page End: 1506
• Publication Date: 2017-11-02
• Subjects: Banach space -- bounded quasi-linear (BQL) generalized inverse with respect to projectors -- complemented subspace -- necessary and sufficient condition; 47A05 -- 46B20; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1344247
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: 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 sufficient 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.