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Original Articles

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

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Pages 1490-1506 | Received 22 Nov 2015, Accepted 15 Jun 2017, Published online: 27 Jul 2017
 

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.

MATHEMATICS SUBJECT CLASSIFICATION:

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