## 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

### Keywords:

Weyl theorem; Riesz idempotent; paranormal operator
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