【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.更多还原

【Abstract】 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.更多还原