$A$-spectral permanence property for $C^*$-algebras

Mohamed Mabrouk; Ali Zamani

$A$-spectral permanence property for $C^*$-algebras

Operator Algebras 2023-05-02 v1 Functional Analysis

Authors: Mohamed Mabrouk , Ali Zamani

Abstract

For a positive element $A$ of a $C^*$ -algebra $\mathfrak{A}$ , let ${\|X\|}_{A}$ denote the $A$ -operator semi-norm of $X\in\mathfrak{A}$ . In this paper, we aim to introduce and study the notion of $A$ -spectrum for $X$ such that ${\|X\|}_{A}<\infty$ . In particular when $A$ is well-supported, we establish an $A$ -spectral permanence property for $C^*$ -algebras.

Keywords

c*-algebra a-spectrum a-operator semi-norm spectral permanence positive element well-supported

Cite

@article{arxiv.2305.00317,
  title  = {$A$-spectral permanence property for $C^*$-algebras},
  author = {Mohamed Mabrouk and Ali Zamani},
  journal= {arXiv preprint arXiv:2305.00317},
  year   = {2023}
}

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15 pages

$A$-spectral permanence property for $C^*$-algebras

Abstract

Keywords

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