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arXiv · 1707.08848

Continuity of spectral radius and type I $C^*$-algebras

Tatiana Shulman
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Abstract

It is shown that the spectral radius is continuous on a $C^*$-algebra if and only if the $C^*$-algebra is type I. This answers a question of V. Shulman and Yu.~Turovskii [10]. It is shown also that the closure of nilpotents in a $C^*$-algebra contains an element with non-zero spectrum if and only if the $C^*$-algebra is not type I.

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Tatiana Shulman. 2017-07-27. Continuity of spectral radius and type I $C^*$-algebras. https://arxiv.org/abs/1707.08848

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