The predual of the space of decomposable maps from a C*-algebra into a von Neumann algebra

摘要

For a C*-algebra A and a von Neumann algebra R, we describe the predual of space D(A,R) of decomposable maps from A into R equipped with decomposable norm. This predual is found to be the matrix regular operator space structure on A?R* with a certain universal property. Its matrix norms are the largest and its positive cones on each matrix level are the smallest among all possible matrix regular operator space structures on A?R* under the two natural restrictions: (1) ||x?y||ε||x||||y|| for xεMk(A),yεMl(R*) and (2) v?w is positive if vεMk(A)+ and wεMl(R*)+.