In terms of the exactly nonzero partition,the reducible projection-system and correlation matrices,two characterizations for a rank three operator in a CSL algebra can be completely decomposed are given.
For finite rank operators in a commutative subspace lattice algebra alg(?)we introduce the concept of correlation matrices,basing on which we prove that a finite rank operator in alg(?)can be written as a finite sum o...For finite rank operators in a commutative subspace lattice algebra alg(?)we introduce the concept of correlation matrices,basing on which we prove that a finite rank operator in alg(?)can be written as a finite sum of rank-one operators in alg(?),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.展开更多
文摘In terms of the exactly nonzero partition,the reducible projection-system and correlation matrices,two characterizations for a rank three operator in a CSL algebra can be completely decomposed are given.
文摘For finite rank operators in a commutative subspace lattice algebra alg(?)we introduce the concept of correlation matrices,basing on which we prove that a finite rank operator in alg(?)can be written as a finite sum of rank-one operators in alg(?),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.
