On single commutators in II_1-factors

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.

10 pages. version 2 modifies somewhat the discussion of Tucci's operators and corrects some minor mistakes. It will appear in Proc. Amer. Math. Soc version 3 adds references and makes minor corrections

References in corpus (1)

• Commutators on ${\ell }_1$