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Isolated point of spectrum ofP-hyponormal, log-hyponormal operators

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Abstract

LetT ∈B(H) be a bounded linear operator on a complex Hilbert spaceH. Let λ0 ∈ σ(T) be an isolated point of σ(T) and let\(E = \frac{1}{{2\pi i}}\int_{\left| {\lambda - \lambda _0 } \right| = r} {\left( {\lambda - T} \right)^{ - 1} d\lambda } \) be the Riesz idempotent for λ0. In this paper, we prove that ifT isp-hyponormal or log-hyponormal, thenE is self-adjoint andE H=ker(H−λ0)=ker(H−λ0 *.

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Authors and Affiliations

  1. Department of Mathematics, Kanagawa University, 221-8686, Yokohama, Japan

    Muneo Chō

  2. Department of Mathematics, Tohoku College of Pharmacy, 981-8558, Sendai, Japan

    Kôtarô Tanahashi

Authors
  1. Muneo Chō
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  2. Kôtarô Tanahashi
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Additional information

This research was supported by Grant-in-Aid Research 1 No. 12640187.

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Chō, M., Tanahashi, K. Isolated point of spectrum ofP-hyponormal, log-hyponormal operators. Integr equ oper theory 43, 379–384 (2002). https://doi.org/10.1007/BF01212700

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