C_0（N）压缩的无界双同态的刻画
Characterization of the unbounded bicommutant of C_0 (N) contractions
摘要：
最近的结果表明，任何闭算子$A$与限制于$K ^2_u := H^2 \ominus u H^2$的后移$S^*$交换，其中$u$是内函数，可以实现为$S^*_u := S^* |_{K^2_u}$的Nevanlinna函数，$A = φ(S^*_u)$，其中$φ$属于依赖于$u$的某类Nevanlinna函数。本文推广了这一结果，证明了给定$C_0 (N)$类的任何压缩$T$，与$T$的交换子交换的任何闭（不一定有界）算子$A$等于$φ(T)$，其中$φ$属于依赖于$T$的极小内函数$m_T$的某类Nevanlinna函数.
英文摘要：
Recent results have shown that any closed operator $A$ commuting with the backwards shift $S^*$ restricted to $K ^2_u := H^2 \ominus u H^2$, where $u$ is an inner function, can be realized as a Nevanlinna function of $S^*_u := S^* |_{K^2_u}$, $A = φ(S^*_u)$, where $φ$ belongs to a certain class of Nevanlinna functions which depend on $u$. In this paper this result is generalized to show that given any contraction $T$ of class $C_0 (N)$, that any closed (and not necessarily bounded) operator $A$ commuting with the commutant of $T$ is equal to $φ(T)$ where $φ$ belongs to a certain class of Nevanlinna functions which depend on the minimal inner function $m_T$ of $T$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
