Canonical operator space structures on non-commutative \(L^p\) spaces (Q1963862)

The author studies canonical operator space structures on the non-commutative spaces \(L^p_\eta(M,\phi,\omega)\) constructed by a Stein-Weiss interpolation procedure. Here, \(\phi\), \(\psi\) are two semifinite faithful weights on a \(W^*\)-algebra \(M\). It is shown that all such spaces for \(0\leq \eta\leq 1\) and arbitrary \(\phi\), \(\psi\) are completely isomorphic as operator spaces, i.e. \(L^p_{\eta_1}(M, \phi_1,\omega_1)\cong L^p_{\eta_2}(M, \phi_2,\omega_2)\). The paper also contains a description of the norms on all matrix spaces of the operator space \(L^p(M)\).