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arXiv · 1807.10395

Range-Kernel Complementation

C. S. Kubrusly
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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

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C. S. Kubrusly. 2018-07-26. Range-Kernel Complementation. https://arxiv.org/abs/1807.10395

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