On the Isolated Points of the Spectrum of Paranormal Operators

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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1. Sendai National College of Technology, Sendai, 989-3128, Japan

   Atsushi Uchiyama

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1. Atsushi Uchiyama
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Correspondence to Atsushi Uchiyama.

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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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• Published: 20 December 2005

• Issue Date: May 2006

• DOI: https://doi.org/10.1007/s00020-005-1386-0

Mathematics Subject Classification (2000).

• Primary 47A10
• Secondary 47B20

Keywords.

• Riesz idempotent
• paranormal operator