Real structure in noncommutative \(L_p\)-spaces (Q6595542)

The paper is devoted to a real counterpart of noncommutative \(L_p\)-spaces associated with von Neumann algebra (they use the term \(W^\ast\)-algebras). The authors define the real valued noncommutative \(L_p\)-spaces associated with semifinite and infinite \(W^\ast\)-algebras and describe their isomorphisms. Also they prove a reduction theorem which approximates real noncommutative \(L_p\)-spaces associated with \(W^\ast\)-algebras of type III by an increasing sequence of real noncommutative \(L_p\)-spaces associated with finite real \(W^\ast\)-algebras