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arXiv · 2009.08977

On the spectral $\nu$-continuity

Salvador Sánchez-Perales·Sergio Palafox·Tomás Pérez-Becerra
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Abstract

In this paper we study the $\nu$-continuity of the spectrum and some of its parts. We show that the approximate point spectrum $\sigma_{ap}$ is upper semi-$\nu$-continuous at every Fredholm operator, then we give sufficient conditions to guarantee the $\nu$-continuity of $\sigma_{ap}$. Also we show that the restriction of the Weyl spectrum on the class of essentially $G_1$ operators is $\nu$-continuous. Finally, we investigate the $\nu$-continuity of the spectrum on the class of $p$-hyponormal operators.

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Salvador Sánchez-Perales, Sergio Palafox, Tomás Pérez-Becerra. 2020-09-18. On the spectral $\nu$-continuity. https://arxiv.org/abs/2009.08977

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