Multiplicative properties of positive maps - Størmer, Erling (MATHEMATICA SCANDINAVICA, 2007)
Let φ be a positive unital normal map of a von Neumann algebra M into itself. It is shown that with some faithfulness assumptions on φ there exists a largest Jordan subalgebra C_φ of M such that the restriction of φ to C_φ is a Jordan automorphism and each weak limit point of (φ^n (a)) for aM belongs to C_φ.