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A remark on non-commutative $L^p$-spaces

Volume 275 / 2024

Shinya Kato, Yoshimichi Ueda Studia Mathematica 275 (2024), 235-248 MSC: Primary 46L51; Secondary 81R15 DOI: 10.4064/sm230724-11-10 Published online: 27 March 2024

Abstract

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

Authors

  • Shinya KatoGraduate School of Mathematics
    Nagoya University
    Nagoya 464-8602, Japan
    e-mail
  • Yoshimichi UedaGraduate School of Mathematics
    Nagoya University
    Nagoya 464-8602, Japan
    e-mail

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