On Finite Rank Operators in CSL Algebras II

For finite rank operators in a commutative subspace lattice algebra algL we introduce the concept of correlation matrices, basing on which we prove that a finite rank operator in algL can be written as a finite sum of rank-one operators in algL, if it has only finitely many different correlation matrices. Thus we can recapture the results of J.R. Ringrose, A.Hopenwasser and R.Moore aa corollaries of our theorems.