Single commutators in C^*-algebras

@misc{cui2026single,
  title = {{Single commutators in $C^*$-algebras}},
  author = {Lu Cui and Minghui Ma},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.14585},
  eprint = {2609.14585},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14585},
}

TY  - UNPB
TI  - Single commutators in C^*-algebras
AU  - Lu Cui
AU  - Minghui Ma
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.14585
UR  - https://arxiv.org/abs/2609.14585
AB  - Let 𝒜 be a simple unital C^*-algebra with real rank zero, nonempty tracial state space 𝒯(𝒜), and strict comparison of projections. We prove that every element T in 𝒜 with τ(T)=0 for all τ∈𝒯(𝒜) is a single commutator if one of the following conditions holds: (1) 𝒜 has unique trace; (2) 𝒜 has stable rank one. We also prove that every nonscalar element in a simple unital purely infinite C^*-algebra is a single commutator. Applications include UHF algebras, irrational rotation algebras, and Cuntz algebras.
ER  -