Larson理想中算子的插值(英文)  

Operator Interpolation in Larson Ideal

作　　者：郭懋正[1] 张小霞[1] 

机构地区：[1]北京大学数学科学学院数学与应用数学实验室

出　　处：《数学进展》2002年第4期323-330,共8页Advances in Mathematics（China）

摘　　要：设A为nest代数,R∞为A的Larson理想,R（A）为A的根,[R（A）]s为R（A）的强拓扑闭.在本文中,我们给出[R（A）]s的纯代数构造;且引进了一个新算子集合I,并证明了:若A的不变子空间格为几乎原子的,则R∞=[R（A）]s=I.利用上述结果,我们研究了当A的不变子空间格为几乎原子时的Larson理想中的算子插值问题.我们得到算子方程AX=Y在R∞中有解A的充分必要条件.Let A be a nest algebra, R∞ its Larson ideal, R(A) its radical and [R(A)]S the strong closure of R(A). In this paper, we study [R(A)]s in a purely algebraic approach, introduce a new operator set X and show that R∞=[R(A)]S =I if the invariant subspace lattice of A is almost atomic. Then we study the operator interpolation problem for Larson ideal R∞ with an almost atomic nest. We obtain necessary and sufficient conditions for bounded linear operators X and Y on a Hilbert space to guarantee the existence of an operator A in R∞ such that AX=Y.

关 键 词：NEST代数 Larson理想 算子插值 纯代数构造 空间格 算子方程 解 

分 类 号：O153[理学—数学]