Bishop’s property (𝛽) and essential spectra of quasisimilar operators

Chen, Lin; Zikun, Yan

doi:10.1090/S0002-9939-99-05047-9

Bishop’s property ($\beta$) and essential spectra of quasisimilar operators
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by Lin Chen and Yan Zikun PDF

Proc. Amer. Math. Soc. 128 (2000), 485-493 Request permission

Abstract:

We analyze the notion of Bishop’s property ($\beta$) to obtain some new concepts. We describe some conditions in terms of these concepts for an operator to have its essential spectrum (spectrum) contained in the essential spectrum (spectrum) of every operator quasisimilar to it. A subfamily of such operators is proved to be dense in $L(\mathbf {H})$.

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