On the Kato, semi-regular and essentially semi-regular spectra

Mohammed Benharrat, Aymen Ammar, Aref Jeribi, Bekkai Messirdi


In this paper, we give some proprieties  of the  semi-regular, essentially semi-regular and the operators of Kato type   on a Banach space. We also show that the essentially semi-regular spectrum of closed, densely defined linear operator is stable under commuting compact perturbation and  its  Kato  spectrum  is stable subjected to additive commuting nilpotent perturbations.

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