Interpolation of quasi noncommutative $L_p$-spaces

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.