Let *Alg* be a nest algebra associated with the nest on a (real or complex) Banach space X. Suppose that there exists a non-trivial idempotent *P Alg* with range *P* (X), and *δ* : *Alg Alg* is a continuous linear mapping (generalized) left derivable at *P*, i.e. *δ*(*ab*) = *aδ*(*b*) + *bδ*(*a*) (*δ*(*ab*) = *aδ*(*b*) + *bδ*(*a*) *baδ*(*I*)) for any *a, b Alg* with *ab* = *P*, where *I* is the identity element of *Alg* . We show that *δ* is a (generalized) Jordan left derivation. Moreover, in a strongly operator topology we characterize continuous linear maps *δ* on some nest algebras *Alg N* with the property that *δ*(*P* ) = 2*P δ*(*P* ) or *δ*(*P* ) = 2*P δ*(*P* ) *− P δ*(*I*) for every idempotent *P* in *Alg N* .

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