Journal of Operator Theory
Volume 72, Issue 1, Summer 2014 pp. 135-158.
Normal limits of nilpotent operators in $C^*$-algebras
Authors:
Paul Skoufranis
Author institution: Department of Mathematics, UCLA, Los Angeles,
California, 90095-1555 U.S.A.
Summary: We will investigate the intersection of the normal
operators with the closure of the nilpotent operators in various
$C^*$-algebras. A complete description of the intersection will be given
for unital, simple, purely infinite $C^*$-algebras. The intersection in AF
$C^*$-algebras is also of interest. In addition, an example of a separable,
nuclear, quasidiagonal $C^*$-algebra where every operator is a limit of
nilpotent operators will be constructed.
DOI: http://dx.doi.org/10.7900/jot.2012nov15.1983
Keywords: $C^*$-algebra, nilpotent operators, quasinilpotent
operators, normal operator, norm-limit, purely infinite $C^*$-algebra
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