A note on the common spectral properties for bounded linear operators

Hassane Zguitti

A note on the common spectral properties for bounded linear operators

Functional Analysis 2019-04-02 v2

Authors: Hassane Zguitti

Abstract

Let $X$ and $Y$ be Banach spaces, $A\,:\,X\rightarrow Y$ and $B,\,C\,:\,Y\rightarrow X$ be bounded linear operators. We prove that if $A(BA)^2=ABACA=ACABA=(AC)^2A,$ then $\sigma_{*}(AC)\setminus\{0\}=\sigma_{*}(BA)\setminus\{0\}$ where $\sigma_*$ runs over a large of spectra originated by regularities.

Keywords

operator theory on banach spaces numerical range banach space

Cite

@article{arxiv.1903.11153,
  title  = {A note on the common spectral properties for bounded linear operators},
  author = {Hassane Zguitti},
  journal= {arXiv preprint arXiv:1903.11153},
  year   = {2019}
}

Comments

11 pages

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