Abstract
Let \((T(t))_{t\ge 0}\) be a \(C_0\)-semigroups and A be its infinitesimal generator. In this work, we prove that the spectral inclusion for \((T(t))_{t\ge 0}\) remains true for the Drazin invertible and quasi-Fredholm spectra. Also, we will give conditions under which facts A is quasi-Fredholm, A is Drazin invertible and A is B-Fredholm are equivalent.
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The authors thank the referees for his suggestions and comments thorough reading of the manuscript.
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Communicated by Poom Kumam.
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Tajmouati, A., Amouch, M. & Alhomidi Zakariya, M.R.F. Spectral Inclusion for \(C_0\)-Semigroups Drazin Invertible and Quasi-Fredholm Operators. Bull. Malays. Math. Sci. Soc. 42, 1383–1392 (2019). https://doi.org/10.1007/s40840-017-0548-y
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DOI: https://doi.org/10.1007/s40840-017-0548-y
Keywords
- Banach space operators
- \(C_0\)-semigroups
- Spectral inclusion
- Drazin invertible operator
- Quasi-Fredholm operator