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PreprintarXiv licencearXiv

Banach non-isomorphism of type III and semifinite noncommutative Lp-spaces

  • Jinghao Huang
  • Fedor Sukochev
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Abstract

Let M be a nonzero type III von Neumann algebra with separable predual, and let N be a semifinite von Neumann algebra. We prove that M* is not isomorphic to a subspace of N*. For 1<p<∞, p≠2, we prove that Lp(M) is not isomorphic to a complemented subspace of Lp(N). In particular, the Banach isomorphism class of Lp(M) distinguishes type III algebras from semifinite algebras for 1≤ p<∞, p≠2.

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Cite

BibTeXRIS
BibTeX
@misc{huang2026banach,
  title = {{Banach non-isomorphism of type III and semifinite noncommutative $L_p$-spaces}},
  author = {Jinghao Huang and Fedor Sukochev},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11055},
  eprint = {2610.11055},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11055},
}
RIS
TY  - UNPB
TI  - Banach non-isomorphism of type III and semifinite noncommutative L_p-spaces
AU  - Jinghao Huang
AU  - Fedor Sukochev
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11055
UR  - https://arxiv.org/abs/2610.11055
AB  - Let M be a nonzero type III von Neumann algebra with separable predual, and let N be a semifinite von Neumann algebra. We prove that M_* is not isomorphic to a subspace of N_*. For 1<p<∞, p≠2, we prove that L_p(M) is not isomorphic to a complemented subspace of L_p(N). In particular, the Banach isomorphism class of L_p(M) distinguishes type III algebras from semifinite algebras for 1≤ p<∞, p≠2.
ER  -