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 $a\in M$ belongs to $C_{φ}$.