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A remark on non-commutative L^p-spaces

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arxiv 2307.01790 v2 pith:YR74YVK2 submitted 2023-07-04 math.OA math-phmath.MP

A remark on non-commutative L^p-spaces

classification math.OA math-phmath.MP
keywords associatednon-commutativespacestensoralgebraalgebrasdescribedescriptions
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We explicitly describe the Haagerup and the Kosaki non-commutative $L^p$-spaces associated with a tensor product von Neumann algebra $M_1\bar{\otimes}M_2$ in terms of those associated with $M_i$ and usual tensor products of unbounded operators. The descriptions are then shown to be useful in the quantum information theory based on operator algebras.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. A general proof of integer R\'enyi QNEC

    hep-th 2026-05 accept novelty 8.0

    Proves integer Rényi QNEC by establishing log-convexity of Kosaki L^n norms under null-translation semigroups for σ-finite von Neumann algebras with half-sided modular inclusions, assuming only finite sandwiched Rényi...

  2. No off-diagonal quantum focusing for R\'enyi divergences

    hep-th 2026-07 accept novelty 7.0

    No Rényi-type divergence obeying DPI, tensor additivity and matched cq conditioning admits a universal off-diagonal quantum focusing inequality.