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Associativity of operator convolutions for group actions on von Neumann algebras

  • Hannes Wendt
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Abstract

Given a pair of commuting, ergodic, trace-preserving and trace-integrable actions of locally compact unimodular groups on a common semifinite von Neumann algebra we prove a form of associativity for convolutions of triples of operators. We view this as a basis for a general version of quantum harmonic analysis.

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Cite

BibTeXRIS
BibTeX
@misc{wendt2026associativity,
  title = {{Associativity of operator convolutions for group actions on von Neumann algebras}},
  author = {Hannes Wendt},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.28445},
  eprint = {2608.28445},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.28445},
}
RIS
TY  - UNPB
TI  - Associativity of operator convolutions for group actions on von Neumann algebras
AU  - Hannes Wendt
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.28445
UR  - https://arxiv.org/abs/2608.28445
AB  - Given a pair of commuting, ergodic, trace-preserving and trace-integrable actions of locally compact unimodular groups on a common semifinite von Neumann algebra we prove a form of associativity for convolutions of triples of operators. We view this as a basis for a general version of quantum harmonic analysis.
ER  -