中文摘要：

设L是可分Hilbert空间上的完全分配交换子空间格,A是Alg L的子代数并且包含Alg L的全体有限秩算子.主要结果是：（1）A上的中心化子是拟空间的;（2）Alg L上的Jordan中心化子是中心化子;（3）当L是套时,Alg L上的Lie中心化子可表示成一个中心化子与一个可加泛函之和的形式,该泛函作用在形如AB-BA的算子上为零.

英文摘要：

Let L be a completely distributive commutative subspace lattice on a separable Hilbert space,A be a subalgebra of Alg L which contains all finite rank operators in Alg L. The main results are as follows：（1） Every centralizer of A is quasi-spatial;（2） Every Jordan centralizer of AlgL must be a centralizer;（3） If L is a nest,then every Lie centralizer of Alg L can be written as a sum of a centralizer and an additive functional on the nest algebra, where the additive functional annihilates operators of the form AB—BA.