Abstract
Let algMβ and algMγ be non-trivial nest subalgebras in factor von Neumann algebra M, and φ be a unital bijection. In this paper, we prove that if φ satisfies φ(A ∘ B) = φ (A) ∘ φ(B) for any A, B ∈ algMβ with AB=0, then φ is either an isomorphism or an anti-isomorphism.
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