Larson理想中算子的插值

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。在文本中，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。

Operator Interpolation in Larson Ideal

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 27 and show that R∞ = [R(A)]s = 27 if the invariant subspace lattice of A is almost atomic. Thenwe 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.