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PreprintCC BY 4.0arXiv

Molnár's Theorem for split C*-by-nilpotent algebras

  • Mario Galici
  • Gianmarco La Rosa
  • Manuel Mancini
  • Gábor P. Nagy
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Abstract

Kubo-Ando means are a rich class of important binary operations on the set of positive elements of an operator algebra. The aim of this article is to understand the algebraic structure of these operations. We generalize a recent result of L. Molnár for C*-algebras to the class of split C*-by-nilpotent algebras by using the method of analytic local expansion of binary operations. Eventually, we prove that in any C*-algebra 𝒜, the identity [x,[y,z]]=0 implies commutativity.

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Cite

BibTeXRIS
BibTeX
@misc{galici2026molnárs,
  title = {{Molnár's Theorem for split $C^*$-by-nilpotent algebras}},
  author = {Mario Galici and Gianmarco La Rosa and Manuel Mancini and Gábor P. Nagy},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08010},
  eprint = {2610.08010},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08010},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Molnár's Theorem for split C^*-by-nilpotent algebras
AU  - Mario Galici
AU  - Gianmarco La Rosa
AU  - Manuel Mancini
AU  - Gábor P. Nagy
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08010
UR  - https://arxiv.org/abs/2610.08010
AB  - Kubo-Ando means are a rich class of important binary operations on the set of positive elements of an operator algebra. The aim of this article is to understand the algebraic structure of these operations. We generalize a recent result of L. Molnár for C^*-algebras to the class of split C^*-by-nilpotent algebras by using the method of analytic local expansion of binary operations. Eventually, we prove that in any C^*-algebra 𝒜, the identity [x,[y,z]]=0 implies commutativity.
ER  -