Haagerup approximation property and positive cones associated with a von Neumann algebra (Q2835235)

The authors introduce the notion of the \(\alpha\)-Haagerup approximation property for \(\alpha \in [0,1/2]\) using a one-parameter family of positive cones studied by \textit{H. Araki} [Pac. J. Math. 50, 309--354 (1974; Zbl 0287.46074)] and show that the \(\alpha\)-Haagerup approximation property does not depend on the choice of \(\alpha\). It suffices to prove that the Haagerup approximation properties introduced in two ways are actually equivalent, one in terms of the standard form and the other in terms of completely positive maps.