On weighted Weyl spectrum, II
Bull. Korean Math. Soc. 2006 Vol. 43, No. 4, 715-722
Printed December 1, 2006
Subhash Chander Arora and Preeti Dharmarha
University of Delhi, University of Delhi
Abstract : In this paper, we show that if $T$ is a hyponormal operator on a non-separable Hilbert space $\mathcal H$, then $\Re\omega_\alpha^0(T)\subset \omega_\alpha^0(\Re T)$, where $\omega_\alpha^0(T)$ is the weighted Weyl spectrum of weight $\alpha$ with $\aleph_0 \le \alpha \le \ h:={\rm dim} \ {\mathcal H}$. 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.
Keywords : weighted spectrum, weighted Weyl spectrum, $\alpha$-Weyl operator
MSC numbers : Primary 47A53
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