On single commutators in II₁–factors

Dykema, Ken; Skripka, Anna

doi:10.1090/S0002-9939-2011-10953-5

On single commutators in II$_1$–factors
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Proc. Amer. Math. Soc. 140 (2012), 931-940 Request permission

Abstract:

We investigate the question of whether all elements of trace zero in a II$_1$–factor are single commutators. We show that all nilpotent elements are single commutators, as are all normal elements of trace zero whose spectral distributions are discrete measures. Some other classes of examples are considered.

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