Almost invertible operators

Zakariae Aznay; Abdelmalek Ouahab; Hassan Zariouh

Almost invertible operators

Spectral Theory 2022-11-16 v1 Functional Analysis

Authors: Zakariae Aznay , Abdelmalek Ouahab , Hassan Zariouh

Abstract

We prove that a bounded linear operator $T$ is a direct sum of an invertible operator and an operator with at most countable spectrum iff $0\notin\mbox{acc}^{\omega_{1}}\,\sigma(T),$ where $\omega_{1}$ is the smallest uncountable ordinal and $\mbox{acc}^{\omega_{1}}\,\sigma(T)$ is the $\omega_{1}$ -th Cantor-Bendixson derivative of $\sigma(T).$

Keywords

numerical range operator theory

Cite

@article{arxiv.2211.07736,
  title  = {Almost invertible operators},
  author = {Zakariae Aznay and Abdelmalek Ouahab and Hassan Zariouh},
  journal= {arXiv preprint arXiv:2211.07736},
  year   = {2022}
}

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