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 for...
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