On weighted Weyl spectrum, II

摘要

In this paper, we show that if $T$ is a hyponormal operator on a non-separable Hilbert space $mathcal H$, then $Reomega_lpha^0(T)subset omega_lpha^0(Re T)$, where $omega_lpha^0(T)$ is the weighted Weyl spectrum of weight $lpha$ with $leph_0 le lpha le h:={m dim} {mathcal H}$. We also give some conditions under which the product of two mbox{$lpha$-Weyl} operators is mbox{$lpha$-Weyl} and its converse implication holds, too. Finally, we show that the weighted Weyl spectrum of a hyponormal operator satisfies the spectral mapping theorem for analytic functions under certain conditions.