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.
出处
《数学进展》
CSCD
北大核心
2002年第4期323-330,共8页
Advances in Mathematics（China）
