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Interpolation of quasi noncommutative $L_p$-spaces

· 2019 · math.OA · arXiv 1905.08491

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abstract

Let $\mathcal{M}$ be a ($\sigma$-finite) von Neumann algebra associated with a normal faithful state $\phi.$ We prove a complex interpolation result for a couple of two (quasi) Haagerup noncommutative $L_p$-spaces $L_{p_0} (\mathcal{M}, \phi)$ and $L_{p_1} (\mathcal{M}, \phi), 0< p_0 < p_1\leq \infty,$ which has further applications to the sandwiched $p$-R\'{e}nyi divergence.

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Relative entropy for von Neumann subalgebras

math.OA · 2019-09-04 · conditional · novelty 7.0

For inclusions of II₁ factors and finite-dimensional algebras, the logarithmic Pimsner-Popa index equals the supremum, over all states and all Rényi parameters p in [1/2,∞], of the sandwiched Rényi relative entropy to the subalgebra.

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  • Relative entropy for von Neumann subalgebras math.OA · 2019-09-04 · conditional · none · ref 18 · internal anchor

    For inclusions of II₁ factors and finite-dimensional algebras, the logarithmic Pimsner-Popa index equals the supremum, over all states and all Rényi parameters p in [1/2,∞], of the sandwiched Rényi relative entropy to the subalgebra.