REMARKS ON POSITIVE CONES ASSOCIATED WITH A VON NEUMANN ALGEBRA

Abstract

Let M be a von Neumann algebra with a cyclic and separating vector ξ₀ and J^# (resp. J^b) be the closure of M₊ξ₀ (resp. M′₊ξ₀). It is shown that the map: ξ∈J^#→ωξ∈M⁺_* is a homeomorphism with respect to the norm topologies. It is also shown that J^# can be replaced by J^b if M is finite.