In this paper, we show that the invertible operator T, which is a bounded linear functional on a separable Hilbert space H, could factor as T = US, where U is unitary and S belongs to width-two CSL algebra algφ （φ ...In this paper, we show that the invertible operator T, which is a bounded linear functional on a separable Hilbert space H, could factor as T = US, where U is unitary and S belongs to width-two CSL algebra algφ （φ = M∨N） when nest M or N is a countable nest, or S belongs to algφ^-1 when nests M and N are countable nests. For the factorization of nest,we obtain that T factors as T = US where S ∈ DN^-1 and U is unitary as N be a countable nest.展开更多
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.
设L是希尔伯特空间H上的一个CSL,A lg L是相应地CSL代数。一族线性映射δ={δn,δn:A lg L→A lg L,n∈N}在Ω∈A lg L Jordan高阶可导,如果对所有n∈N,∑i+j=n[δi(A)δj(B)+δj(B)δi(A)]=δ(Ω),其中A,B∈A lg L,AB+BA=Ω。给出了一...设L是希尔伯特空间H上的一个CSL,A lg L是相应地CSL代数。一族线性映射δ={δn,δn:A lg L→A lg L,n∈N}在Ω∈A lg L Jordan高阶可导,如果对所有n∈N,∑i+j=n[δi(A)δj(B)+δj(B)δi(A)]=δ(Ω),其中A,B∈A lg L,AB+BA=Ω。给出了一族线性映射δ={δn:A lg L→A lg L}在0点Jordan高阶可导的充要条件。利用此结果证明了不可约CDCSL代数,因子von Neumann代数上的套子代数(特别地,希尔伯特空间套代数)到其自身的一族线性映射δ={δn,n∈N}在0点Jordan高阶可导当且仅当它是一个高阶导子。展开更多
The authors prove that all n-th completely bounded cohomology groups of a nest algebra T（N） acting on a separable Hilbert space are trivial when the coefficients lie in any ultraweakly closed T（N）-bimodule contain...The authors prove that all n-th completely bounded cohomology groups of a nest algebra T（N） acting on a separable Hilbert space are trivial when the coefficients lie in any ultraweakly closed T（N）-bimodule containing the nest algebra. They also prove that Hcb^n（A, M） ≌ Hcb^n（A, M） for all n ≥ 1 and a CSL algebra .A with an ultraweakly closed .A-bimodul.M containing A.展开更多
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
基金Supported by the National Science Foundation of China(90205019)
文摘In this paper, we show that the invertible operator T, which is a bounded linear functional on a separable Hilbert space H, could factor as T = US, where U is unitary and S belongs to width-two CSL algebra algφ （φ = M∨N） when nest M or N is a countable nest, or S belongs to algφ^-1 when nests M and N are countable nests. For the factorization of nest,we obtain that T factors as T = US where S ∈ DN^-1 and U is unitary as N be a countable nest.
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.
文摘设L是希尔伯特空间H上的一个CSL,A lg L是相应地CSL代数。一族线性映射δ={δn,δn:A lg L→A lg L,n∈N}在Ω∈A lg L Jordan高阶可导,如果对所有n∈N,∑i+j=n[δi(A)δj(B)+δj(B)δi(A)]=δ(Ω),其中A,B∈A lg L,AB+BA=Ω。给出了一族线性映射δ={δn:A lg L→A lg L}在0点Jordan高阶可导的充要条件。利用此结果证明了不可约CDCSL代数,因子von Neumann代数上的套子代数(特别地,希尔伯特空间套代数)到其自身的一族线性映射δ={δn,n∈N}在0点Jordan高阶可导当且仅当它是一个高阶导子。
基金Supported partially by NSF of China (10201007)National Tianyuan Foundation of China (A0324614)
文摘The authors prove that all n-th completely bounded cohomology groups of a nest algebra T（N） acting on a separable Hilbert space are trivial when the coefficients lie in any ultraweakly closed T（N）-bimodule containing the nest algebra. They also prove that Hcb^n（A, M） ≌ Hcb^n（A, M） for all n ≥ 1 and a CSL algebra .A with an ultraweakly closed .A-bimodul.M containing A.
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.
