论文标题
非交通单位行球中的亚速度希尔伯特空间
Sub-Hardy Hilbert spaces in the non-commutative unit row-ball
论文作者
论文摘要
In the classical Hardy space theory of square-summable Taylor series in the complex unit disk there is a circle of ideas connecting Szegö's theorem, factorization of positive semi-definite Toeplitz operators, non-extreme points of the convex set of contractive analytic functions, de Branges--Rovnyak spaces and the Smirnov class of ratios of bounded analytic functions in the disk.我们将这些想法扩展到完整的Fock空间的多变量和非共同设置，该设置在几个非交换变量中被标识为Square-ummable Power系列的\ Emph {free Hardy Space}。作为应用程序，我们证明了用于非共同合理函数的Fejér-Riesz样式定理。
In the classical Hardy space theory of square-summable Taylor series in the complex unit disk there is a circle of ideas connecting Szegö's theorem, factorization of positive semi-definite Toeplitz operators, non-extreme points of the convex set of contractive analytic functions, de Branges--Rovnyak spaces and the Smirnov class of ratios of bounded analytic functions in the disk. We extend these ideas to the multi-variable and non-commutative setting of the full Fock space, identified as the \emph{free Hardy space} of square-summable power series in several non-commuting variables. As an application, we prove a Fejér-Riesz style theorem for non-commutative rational functions.
