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arXiv · 2305.00317

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

Mohamed Mabrouk·Ali Zamani
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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.

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Mohamed Mabrouk, Ali Zamani. 2023-04-29. $A$-spectral permanence property for $C^*$-algebras. https://arxiv.org/abs/2305.00317

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