Abstract.
For paranormal operator T on a separable complex Hilbert space \(\mathcal{H},\) we show that (1) Weyl’s theorem holds for T, i.e., σ(T) \ w(T) = π00(T) and (2) every Riesz idempotent E with respect to a non-zero isolated point λ of σ(T) is self-adjoint (i.e., it is an orthogonal projection) and satisfies that ranE = ker(T − λ) = ker(T − λ)*.
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Uchiyama, A. On the Isolated Points of the Spectrum of Paranormal Operators. Integr. equ. oper. theory 55, 145–151 (2006). https://doi.org/10.1007/s00020-005-1386-0
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DOI: https://doi.org/10.1007/s00020-005-1386-0