Convex Sequential Product Automorphisms on the Positive Cone of a Factor von Neumann Algebra
Let M be a factor von Neumann algebra on a complex Hilbert space H with dim M＞1 and M+the positive cone of M.We consider automorphisms of M+with respect to convex sequential product oλ on M+for some λ ∈[0,1]defined by AoλB=λA1/2BA1/2+(1-λ)B1/2AB1/2 for any A,B ∈ M+.We show that an automorphism of M+with respect to convex sequential product is implemented by a*-isomorphism or an anti-*-isomorphism of M.
factor von Neumann algebrapositive coneconvex sequential productautomorphism
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