Closed Complemented Subspaces of Banach Spaces and Existence of Bounded Quasi-linear Generalized Inverses |
| |
| Authors: | Liu Guanqi Henryk Hudzik |
| |
| Institution: | 1. Yuan Yung Tseng Functional Analysis Research Center, Harbin Normal University, Harbin, P.R. China;2. School of Mathematics and Statistics, Northeast Normal University, Changchun, P.R. China;3. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland |
| |
| 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 su?cient 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. |
| |
| Keywords: | Banach space bounded quasi-linear (BQL) generalized inverse with respect to projectors complemented subspace necessary and sufficient condition |
|
|
