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arXiv · 1205.3537

Normal Limits of Nilpotents in C*-Algebras

Paul Skoufranis
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Abstract

We will investigate the intersection of the normal operators with the closure of the nilpotent and quasinilpotent operators in various C*-algebras. A complete characterization will be given for type I and type III von Neumann algebras with separable predual and for unital, simple, purely infinite C*-algebras. Some restrictions that prevent normal operators from being limits of quasinilpotent operators will be given. The case of AF C*-algebras will be of particular interest. In addition, the closure of the span of the nilpotent operators and the distance from a projection to the nilpotent operators of various C*-algebras will be examined.

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Paul Skoufranis. 2013-12-02. Normal Limits of Nilpotents in C*-Algebras. https://doi.org/10.7900/jot.2012nov15.1983

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