Abstract.
Let T be a w-hyponormal operator on a Hilbert space H, \(\widetilde T\) its Aluthge transform, λ an isolated point of the spectrum of T, and Eλ and \( \widetilde E_{\lambda }\) the Riesz idempotents, with respect to λ, of T and \( \widetilde T, \) respectively. It is shown that \(E_{\lambda } H = \widetilde E_{\lambda } H.\) Consequently, Eλ is self-adjoint, \(E_{\lambda } = \widetilde E_{\lambda } \) and \( E_{\lambda } H = \ker (T - \lambda ) = \ker (T - \lambda )^*\) if λ ≠ 0. Moreover, it is shown that Weyl’s theorem holds for f(T), where f ∈ H(σ (T)).
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Han, Y.M., Lee, J.I. & Wang, D. Riesz Idempotent and Weyl’s Theorem for w-hyponormal Operators. Integr. equ. oper. theory 53, 51–60 (2005). https://doi.org/10.1007/s00020-003-1313-1
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DOI: https://doi.org/10.1007/s00020-003-1313-1