Abstract
Let ϕ be a surjective Jordan homomorphism from a nest algebra AlgN onto another nest algebra AlgM. It is showed that ϕ is a homomorphism, or ϕ is an anti-homomorphism, or ϕ(N)={0,I}. Furthermore, if AlgN is of infinite multiplicity, then ϕ is either a homomorphism or an anti-homomorphism.
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