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PreprintarXiv licencearXiv

The Operator Daugavet Property in Semifinite Noncommutative L1-Spaces

  • Junxiang Qi
  • Qi Liu
  • Yongjin Li
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Abstract

Let ℳ be a diffuse semifinite von Neumann algebra endowed with a faithful normal semifinite trace τ. We prove that, for every nonzero Banach space Y, the projective tensor product L1(ℳ,τ)⊗̂πY has the operator Daugavet property. Moreover, the witnessing operators may always be chosen contractive. This extends the operator Daugavet phenomenon from atomless vector-valued L1-spaces to the semifinite noncommutative setting and yields further Daugavet-type consequences for projective symmetric tensor products, all without approximation assumptions.

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Cite

BibTeXRIS
BibTeX
@misc{qi2026operator,
  title = {{The Operator Daugavet Property in Semifinite Noncommutative $L_1$-Spaces}},
  author = {Junxiang Qi and Qi Liu and Yongjin Li},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18044},
  eprint = {2609.18044},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18044},
}
RIS
TY  - UNPB
TI  - The Operator Daugavet Property in Semifinite Noncommutative L_1-Spaces
AU  - Junxiang Qi
AU  - Qi Liu
AU  - Yongjin Li
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.18044
UR  - https://arxiv.org/abs/2609.18044
AB  - Let ℳ be a diffuse semifinite von Neumann algebra endowed with a faithful normal semifinite trace τ. We prove that, for every nonzero Banach space Y, the projective tensor product L_1(ℳ,τ)⊗̂_πY has the operator Daugavet property. Moreover, the witnessing operators may always be chosen contractive. This extends the operator Daugavet phenomenon from atomless vector-valued L_1-spaces to the semifinite noncommutative setting and yields further Daugavet-type consequences for projective symmetric tensor products, all without approximation assumptions.
ER  -