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

Authors:	Muneo Ch and Kôtarô Tanahashi

Institution:	(1) Department of Mathematics, Kanagawa University, 221-8686 Yokohama, Japan;(2) Department of Mathematics, Tohoku College of Pharmacy, 981-8558 Sendai, Japan

Abstract:	LetT B(H) be a bounded linear operator on a complex Hilbert spaceH. Let ₀ (T) be an isolated point of (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 ₀. In this paper, we prove that ifT isp-hyponormal or log-hyponormal, thenE is self-adjoint andE H=ker(H–₀)=ker(H–₀ ^*.This research was supported by Grant-in-Aid Research 1 No. 12640187.

Keywords:	47A10 47B20
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