Bulletin of the Korean Mathematical Society ( Vol.43 NO.4 / 2006 ) Title On weighted Weyl spectrum, II(ENG) Author Subhash Chander Arora ,Preeti Dharmarha  MSC 47A53 Publication Page 715-722 Page Abstract 1. Introduction 2. Operator satisfying $Reomega_alpha^0(T)subset omega_alpha^0(Re T)$ 3. The product of $alpha$-Weyl operators 4. Spectral mapping theorem Own Status Keyword weighted spectrum, weighted Weyl spectrum, $alpha$-Weyl operator Note Summary In this paper, we show that if $T$ is a hyponormal operator on a non-separable Hilbert space $mathcal H$, then $Reomega_alpha^0(T)subset omega_alpha^0(Re T)$, where $omega_alpha^0(T)$ is the weighted Weyl spectrum of weight $alpha$ with $aleph_0 le alpha le h:={ m dim} {mathcal H}$. We also give some conditions under which the product of two mbox{$alpha$-Weyl} operators is mbox{$alpha$-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. Attach [DVI]  [PDF]