Generalized interpolation in finite maximal subdiagonal algebras
Generalized interpolation in finite maximal subdiagonal algebras
复制标题
有限最大次对角代数中的广义插值
DOI：
10.1017/s0305004100072893
复制
发表时间：
1995
影响因子：
0.8
通讯作者：
K. Saito
中科院分区：
文献类型：
--
作者：
K. Saito
自1960年Kadison和Singer的论文以来，非自伴算子代数一直被研究。在文献[1]中，Arveson引入了次对角代数的概念作为弱 *-Dirichlet代数的推广，并研究了算子代数的解析性。在此之后，我们在这一方向上又有了许多关于非自伴代数的文章：套代数、CSL代数、自反代数、解析算子代数、解析交叉积等等。由于次对角代数的概念是弱 *-Dirichlet代数的类似，所以从函数代数的理论出发，次对角代数具有许多富有成果的性质。因此，我们在这个方向上有几个尝试：不变子空间的Beurling-Lax-Halmos定理，极大性，因子分解定理等等。
Non-selfadjoint operator algebras have been studied since the paper of Kadison and Singer in 1960. In [1], Arveson introduced the notion of subdiagonal algebras as the generalization of weak *-Dirichlet algebras and studied the analyticity of operator algebras. After that, we have many papers about non-selfadjoint algebras in this direction: nest algebras, CSL algebras, reflexive algebras, analytic operator algebras, analytic crossed products and so on. Since the notion of subdiagonal algebras is the analogue of weak *-Dirichlet algebras, subdiagonal algebras have many fruitful properties from the theory of function algebras. Thus, we have several attempts in this direction: Beurling–Lax–Halmos theorem for invariant subspaces, maximality, factorization theorem and so on.