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On the isolated points of the spectrum of paranormal operators. (English) Zbl 1105.47021

Let \(T\) be a paranormal operator on a separable complex Hilbert space. The author shows (i) an equivalent condition for paranormality of \(T\) via the matrix representation of \(T\), (ii) Weyl’s theorem holds for \(T\), and (iii) every Riesz idempotent \(E\) with respect to a nonzero isolated point \(\lambda\) of \(\sigma(T)\) is selfadjoint and satisfies ran\(E=\ker (T-\lambda)=\ker(T-\lambda)^{*}\). For a hyponormal operator \(T\), the above results have already been shown, and the author extends the assumption to paranormality of \(T\).

MSC:

47B20 Subnormal operators, hyponormal operators, etc.
47A10 Spectrum, resolvent
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