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
We show in a certain Lie-algebra, the connections between the Lie subalgebra G＋ ：= G-t-G＊ 4- [G, G＊], generated by a Lie subalgebra G, and the properties of G. This allows us to investigate some useful information...We show in a certain Lie-algebra, the connections between the Lie subalgebra G＋ ：= G-t-G＊ 4- [G, G＊], generated by a Lie subalgebra G, and the properties of G. This allows us to investigate some useful information about the structure of such two Lie subalgehras. Some results on the relations between the two Lie subalgebras are obtained. As an application, we get the following conclusion： Let ,4 C /3（2d） be a space of self-adjoint operators and L： ：= A ~ i^4 the corresponding complex Lie＊-algebra. G＋ = G 4- G＊ 4- [G, G＊] and G are two LM-decomposable Lie subalgebras of L： with the decomposition 6＋ = 7^（6＋） 4- S, G -- T~~ 4- 86, and T^6 C T^（6＋）. Then 6＋ is ideally finite iff T~ ：= 7~6 4- ~ 4- [T^6,7~] is a quasisolvable Lie subalgebra, S^- ：= 86 4- S~ 4- [$6, $~] is an ideally finite semisimple Lie subalgebra, and [7~6,86] = [R.~, 86] = {0}.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.
基金Supported by National Natural Science Foundation of China （Grant No. 10571011）
文摘We show in a certain Lie-algebra, the connections between the Lie subalgebra G＋ ：= G-t-G＊ 4- [G, G＊], generated by a Lie subalgebra G, and the properties of G. This allows us to investigate some useful information about the structure of such two Lie subalgehras. Some results on the relations between the two Lie subalgebras are obtained. As an application, we get the following conclusion： Let ,4 C /3（2d） be a space of self-adjoint operators and L： ：= A ~ i^4 the corresponding complex Lie＊-algebra. G＋ = G 4- G＊ 4- [G, G＊] and G are two LM-decomposable Lie subalgebras of L： with the decomposition 6＋ = 7^（6＋） 4- S, G -- T~~ 4- 86, and T^6 C T^（6＋）. Then 6＋ is ideally finite iff T~ ：= 7~6 4- ~ 4- [T^6,7~] is a quasisolvable Lie subalgebra, S^- ：= 86 4- S~ 4- [$6, $~] is an ideally finite semisimple Lie subalgebra, and [7~6,86] = [R.~, 86] = {0}.
