论文标题
每个完整的选择空间都满足列行属性
Every complete Pick space satisfies the column-row property
论文作者
论文摘要
在完整的选择空间的理论中，列行属性已出现在各种情况下。我们表明，通过以下强形式以每个完整的挑选空间满足：诱导承包列乘法运算符的每个乘数序列也会诱导承包行乘法运算符。结合已知结果，这会产生许多后果。首先，我们获得了弱产品空间理论的多个应用，包括分解，乘数和不变子空间。其次，在分离和Carleson测量条件方面对插值序列的表征有一个简短的证明，而与Kadison-Singer问题的解决方案无关。第三，我们发现在球上的de Branges-Rovnyak空间理论中，陪审团和马丁的圆柱乘数正是乘数代数的单位球的极端点。
In the theory of complete Pick spaces, the column-row property has appeared in a variety of contexts. We show that it is satisfied by every complete Pick space in the following strong form: each sequence of multipliers that induces a contractive column multiplication operator also induces a contractive row multiplication operator. In combination with known results, this yields a number of consequences. Firstly, we obtain multiple applications to the theory of weak product spaces, including factorization, multipliers and invariant subspaces. Secondly, there is a short proof of the characterization of interpolating sequences in terms of separation and Carleson measure conditions, independent of the solution of the Kadison-Singer problem. Thirdly, we find that in the theory of de Branges-Rovnyak spaces on the ball, the column-extreme multipliers of Jury and Martin are precisely the extreme points of the unit ball of the multiplier algebra.
