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 as corollaries of our theorems. Research supported by NSF of China