REAL STRUCTURE IN NONCOMMUTATIVE Lp-SPACES

Our work is devoted to the construction of real valued noncommutative L-p spaces associated with real W*-algebras of different types. We construct such real noncommutative L-p-spaces, 1 <= p < infinity, and we prove the theorem of isomorphism for real noncommutative L-p-spaces. Finally, we build an approximation of L-p-spaces associated with real W *-algebras of type III via L-p-spaces associated with finite real W *-algebras, analogously to the work of U. Haagerup, M. Junge and Q. Xu