Interpolation in the noncommutative Schur-Agler class
Interpolation in the noncommutative Schur-Agler class
复制标题
非交换 Schur-Agler 类中的插值
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
V. Bolotnikov
中科院分区：
文献类型：
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作者：
J. Ball;V. Bolotnikov
定义域D上的Schur-Agler函数类为D上的全纯算子值函数类，当变量插入满足某种多项式范数不等式的算子交换元组时，满足某种von Neumann不等式.现在已经介绍了一个非交换版本的Schur-Agler类，它由非交换不定式中的形式幂级数组成，当来自非交换算子球的算子元组（不一定是交换的）插入形式不定式时，它满足冯诺依曼不等式的非交换版本。本文的目的是将以前开发的插值理论的交换Schur-Agler类，这个非交换设置。
The class of Schur-Agler functions over a domainD C d is de- fined as the class of holomorphic operator-valued functions onD for which a certain von Neumann inequality is satisfied when a commuting tuple of operators satisfying a certain polynomial norm inequality is plugged in for the variables. There now has been introduced a noncommutative version of the Schur-Agler class which consists of formal power series in noncommuting indeterminates satisfying a noncommutative version of the von Neumann in- equality when a tuple of operators (not necessarily commuting) coming from a noncommutative operator ball is plugged in for the formal indeterminates. The purpose of this paper is to extend the previously developed interpolation theory for the commutative Schur-Agler class to this noncommutative setting.