Range-Kernel Complementation
Functional Analysis
2020-10-28 v2
Abstract
If a Banach-space operator has a complemented range, then its normed-space adjoint has a complemented kernel and the converse holds on a reflexive Banach space. It is also shown when complemented kernel for an operator is equivalent to complemented range for its normed-space adjoint. This is applied to compact operators and to compact perturbations. In particular, compact perturbations of semi-Fredholm operators have complemented range and kernel for both the perturbed operator and its normed-space adjoint
Cite
@article{arxiv.1807.10395,
title = {Range-Kernel Complementation},
author = {C. S. Kubrusly},
journal= {arXiv preprint arXiv:1807.10395},
year = {2020}
}