If a Banach-space operator has a complemented range, then its normed-space adjoint has a complemented kernel and the converse holds on a re exive 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.
Aiena, P., Fredholm and Local Spectral Theory, with Applications to Multipliers, Kluwer-Springer, New York, 2004.
Aiena, P., Fredholm and Local Spectral Theory, with Applications to Multipliers, Kluwer-Springer, New York, 2004.)| false
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Studia Scientiarum Mathematicarum Hungarica
2021 Volume 58
Magyar Tudományos Akadémia
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