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

LetT (element of)B(H) be a bounded linear operator on a complex Hilbert spaceH. Let (lambda)0 (element of)(sigma)(T) be an isolated point of (sigma)(T) and let E=1/2*(pi)*i(integral)((lambda)-T)^-1d(lambda) be the Riesz idempotent for (lambda)0. In this paper, we prove that ifT isp-hyponormal or log-hyponormal, thenE is self-adjoint andE H=ker(H–(lambda)0)=ker(H–(lambda)0 *.