• Title, Summary, Keyword: weighted Weyl spectrum

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ON WEIGHTED WEYL SPECTRUM, II

  • Arora Subhash Chander;Dharmarha Preeti
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.4
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    • pp.715-722
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    • 2006
  • In this paper, we show that if T is a hyponormal operator on a non-separable Hilbert space H, then $Re\;{\omega}^0_{\alpha}(T)\;{\subset}\;{\omega}^0_{\alpha}(Re\;T)$, where ${\omega}^0_{\alpha}(T)$ is the weighted Weyl spectrum of weight a with ${\alpha}\;with\;{\aleph}_0{\leq}{\alpha}{\leq}h:=dim\;H$. We also give some conditions under which the product of two ${\alpha}-Weyl$ operators is ${\alpha}-Weyl$ 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.