中文摘要：

Let N be a nest on a Banach space X,and AlgN be the associated nest algebra.It is shown that,if there exists a non-trivial element N in N which is complemented in X and dim N = 1,then every additive biderivation from AlgN into itself is an inner biderivation.Based on this result,we give characterizations of centralizing(commuting) maps,cocentralizing derivations,and cocommuting generalized derivations on nest algebras.

英文摘要：

Let N be a nest on a Banach space X, and AlgN be the associated nest algebra. It is shown that, if there exists a non-trivial element N in N which is complemented in X and dim N ≠ 1, then every additive biderivation from AlgN into itself is an inner biderivation. Based on this result, we give characterizations of centralizing （commuting） maps, cocentraliz-ing derivations, and cocommuting generalized derivations on nest algebras.