Nest代数上的在零点广义可导映射

设A为B（H）的子代数,　是A到B（H）的线性映射,我们说　在0点广义可导（广义双边可导）,如果对任意的S,T∈A且ST=0（ST=0或TS=0）,有　（ST）=　（S）T+S　（T）-S　（I）T.本文主要得到如下结果:（1）有限Nest代数上的每个范数拓扑连续的在0点广义可导的线性映射是广义内导子;（2）若N是完备Nest且H_　 H,则algN上的每个范数拓扑连续的在0点广义双边可导的线性映射是广义内导子.     

二宽度CSL代数的直和分解

本文给出了可分Ｈｉｌｂｅｒｔ空间上的二宽度ＣＳＬ代数分解成其对角与它的一个范数闭理想（即满足Ｒｉｎｇｒｏｓｅ条件的算子集）直和的充要条件是：此二宽度ＣＳＬ是由一个有限ＣＳＬ与一个有补ＣＳＬ生成的．     

All-derivable points in nest algebras

Suppose that A is an operator algebra on a Hilbert space H. An element V in A is called an all-derivable point of A for the strong operator topology if every strong operator topology continuous derivable mapping φ at V is a derivation. Let N be a complete nest on a complex and separable Hilbert space H. Suppose that M belongs to N with {0}≠M≠H and write for M or M^⊥. Our main result is: for any with , if is invertible in , then Ω is an all-derivable point in for the strong operator topology.     

导子的范数估计

本文给出了因子 ｖｏｎ Ｎｅｕｍａｎｎ代数中套子代数上导子的范数估计．利用此结果得到一个距离公式,并证明了因子 ｖｏｎ Ｎｅｕｍａｎｎ代数中的任何套子代数都具有ＡＩＰ（ｒ, ｓ）性质     

Derivations and isomorphisms of certain reflexive operator algebras

In this paper, we will prove that every derivation of completely distributive subspace lattice (CDS) algebras on Banach space is automatically continuous. This is new even in the Hilbert space case. As an application of this result, we obtain that every additive derivation of nest algebras on Banach spaces is inne. We will also prove that every isomorphism between nest algebras on Banach space is automatically continuous, and in addition, is spatial. Research supported by NSF of China and YSF of Shandong     

Invariant linear manifolds for CSL-algebras and nest algebras

Every invariant linear manifold for a CSL-algebra, , is a closed subspace if, and only if, each non-zero projection in is generated by finitely many atoms associated with the projection lattice. When is a nest, this condition is equivalent to the condition that every non-zero projection in has an immediate predecessor ( is well ordered). The invariant linear manifolds of a nest algebra are totally ordered by inclusion if, and only if, every non-zero projection in the nest has an immediate predecessor.     

Nests with the partial factorization property

It is proved that a nest on a separable complex Hilbert space has the left (resp. right) partial factorization property, which means that for every invertible operator from onto a Hilbert space there exists an isometry (resp. a coisometry) from into such that both and are in the associated nest algebra if and only if it is atomic (resp. countable).

     

Interpolation in nest algebra modules

Let be a nest algebra and its invariant projection (or subspace) lattice. In this paper, using order homomorphisms of , we give necessary and sufficient conditions on bounded linear operators and on a Hilbert space to guarantee the existence of an operator in a certain -module such that .

     

Intersections of nest algebras in finite dimensions

If are maximal nests on a finite-dimensional Hilbert space H, the dimension of the intersection of the corresponding nest algebras is at least dim H. On the other hand, there are three maximal nests whose nest algebras intersect in the scalar operators. The dimension of the intersection of two nest algebras (corresponding to maximal nests) can be of any integer value from n to n(n+1)/2, where n=dim H. For any two maximal nests there exists a basis {f₁,f₂,…,f_n} of H and a permutation π such that and where M_i=  span{f₁,f₂,…,f_i} and N_i= span{f_π(1),f_π(2),…,f_π(i)}. The intersection of the corresponding nest algebras has minimum dimension, namely dim H, precisely when π(j)=n−j+1,1jn. Those algebras which are upper-triangular matrix incidence algebras, relative to some basis, can be characterised as intersections of certain nest algebras.     

Additive maps preserving Jordan zero-products on nest algebras

Let and be nest algebras associated with the nests and on Banach Spaces. Assume that and are complemented whenever N_-=N and M_-=M. Let be a unital additive surjection. It is shown that Φ preserves Jordan zero-products in both directions, that is Φ(A)Φ(B)+Φ(B)Φ(A)=0AB+BA=0, if and only if Φ is either a ring isomorphism or a ring anti-isomorphism. Particularly, all unital additive surjective maps between Hilbert space nest algebras which preserves Jordan zero-products are characterized completely.