Uchiyama, Atsushi On the isolated points of the spectrum of paranormal operators. (English) Zbl 1105.47021 Integral Equations Oper. Theory 55, No. 1, 145-151 (2006). 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 \(T\). Reviewer: Takeaki Yamazaki (Yokohama) Cited in 1 ReviewCited in 16 Documents MSC: 47B20 Subnormal operators, hyponormal operators, etc. 47A10 Spectrum, resolvent Keywords:Weyl theorem; Riesz idempotent; paranormal operator PDFBibTeX XMLCite \textit{A. Uchiyama}, Integral Equations Oper. Theory 55, No. 1, 145--151 (2006; Zbl 1105.47021) Full Text: DOI