Abstract
We know that an operator T acting on a Banach space satisfying generalized Weyl’s theorem also satisfies Weyl’s theorem. Conversely we show that if all isolated eigenvalues of T are poles of its resolvent and if T satisfies Weyl’s theorem, then it also satisfies generalized Weyl’s theorem. We give also a similar result for the equivalence of a–Weyl’s theorem and generalized a–Weyl’s theorem. Using these results, we study the case of polaroid operators, and in particular paranormal operators.
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Supported by Protars D11/16 and Project P/201/03 (Morocco–Spain(AECI))
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Berkani, M. On the Equivalence of Weyl Theorem and Generalized Weyl Theorem. Acta Math Sinica 23, 103–110 (2007). https://doi.org/10.1007/s10114-005-0720-4
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DOI: https://doi.org/10.1007/s10114-005-0720-4
Keywords
- B–Fredholm operator
- Weyl’s theorem
- generalized Weyl’s theorem
- a–Weyl’s theorem
- generalized a–Weyl’s theorem
- poles