ON WEIGHTED WEYL SPECTRUM, II

Title & Authors
ON WEIGHTED WEYL SPECTRUM, II
Arora Subhash Chander; Dharmarha Preeti;

Abstract
In this paper, we show that if T is a hyponormal operator on a non-separable Hilbert space H, then $\small{Re\;{\omega}^0_{\alpha}(T)\;{\subset}\;{\omega}^0_{\alpha}(Re\;T)}$, where $\small{{\omega}^0_{\alpha}(T)}$ is the weighted Weyl spectrum of weight a with $\small{{\alpha}\;with\;{\aleph}_0{\leq}{\alpha}{\leq}h:=dim\;H}$. We also give some conditions under which the product of two $\small{{\alpha}-Weyl}$ operators is $\small{{\alpha}-Weyl}$ 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;$\small{{\alpha}-Weyl}$ operator;
Language
English
Cited by
1.
On <i>α</i>-Weyl Operators, Advances in Pure Mathematics, 2016, 06, 03, 138
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