Abstract
It is well known that an hyponormal operator satisfies Weyl’s theorem. A result due to Conway shows that the essential spectrum of a normal operator N consists precisely of all points in its spectrum except the isolated eigenvalues of finite multiplicity, that’s \(\sigma _{e}(N)=\sigma (N)\setminus E^0(N).\) In this paper, we define and study a new class named \((W_{e})\) of operators satisfying \(\sigma _{e}(T)=\sigma (T)\setminus E^0(T),\) as a subclass of (W). A counterexample shows generally that an hyponormal does not belong to the class \((W_{e}),\) and we give an additional hypothesis under which an hyponormal belongs to the class \((W_{e}).\) We also give the generalization class \((gW_{e})\) in the context of B-Fredholm theory, and we characterize \((B_{e}),\) as a subclass of (B), in terms of localized SVEP.
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Aznay, Z., Zariouh, H. On the class of \((W_{e})\)-operators. Rend. Circ. Mat. Palermo, II. Ser 72, 1363–1376 (2023). https://doi.org/10.1007/s12215-022-00737-8
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DOI: https://doi.org/10.1007/s12215-022-00737-8