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ON WEIGHTED WEYL SPECTRUM, II

  • Arora Subhash Chander ;
  • Dharmarha Preeti
  • Published : 2006.11.30

Abstract

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.

Keywords

weighted spectrum;weighted Weyl spectrum;${\alpha}-Weyl$ operator

References

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Cited by

  1. On <i>α</i>-Weyl Operators vol.06, pp.03, 2016, https://doi.org/10.4236/apm.2016.63011