English

On single commutators in II_1-factors

Operator Algebras 2011-02-08 v3

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.

Cite

@article{arxiv.1007.1701,
  title  = {On single commutators in II_1-factors},
  author = {Ken Dykema and Anna Skripka},
  journal= {arXiv preprint arXiv:1007.1701},
  year   = {2011}
}

Comments

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

R2 v1 2026-06-21T15:46:40.584Z