On the Banach-isomorphic classification of \(L_p\) spaces of hyperfinite von Neumann algebras (Q2704627)

The authors announce a complete Banach space classification of \(L_p\) spaces associated with semifinite hyperfinite von Neumann algebras. Each such space (\(p\neq 2\)) is isomorphic to one of the following, pairwise non-isomorphic, spaces: \(\ell_p\), \(L_p\), \(S_p\), \(C_p\), \(S_p\oplus L_p\), \(L_p(S_p)\), \(C_p\oplus L_p\), \(L_p(C_p)\), \(C_p\oplus L_p(S_p)\), \({\L}_p({\mathcal R})\), \(C_p\oplus{\L}_p({\mathcal R})\), \({\L}_p({\mathcal R})\oplus L_p(C_p)\), \({\L}_p({\mathcal R}_{0,1})\). Here \(S_p\) is the \(L_p\) space associated with the von Neumann algebra \(\bigoplus_{n=1}^\infty M_n\).