论文标题
移动半群的几乎不变子空间
Nearly invariant subspaces for shift semigroups
论文作者
论文摘要
令$ \ {t（t）\} _ {t \ geq0} $为$ c_0 $ -semigroup在无限尺寸可分离的希尔伯特空间上；本文介绍了亚平方空间的$ \ {t（t）^*\} _ {t \ geq0} $不变性的合适定义。最小值的一系列原型示例几乎$ \ {s（t）^*\} _ {t \ geq0} $不变的子空间用于换档半群$ \ {s（t）\ {t）_ {t \ geq0} $ on $ l^2（0，\ infty）$ in Covern $ nive in of closeject与内部功能$θ$相关的Toeplitz运算符的单元磁盘的空间。尤其是，右半平面和单位磁盘的耐力空间上的相应子空间与模型空间有关。这项工作进一步包括讨论与耐力空间中与模型空间相关的某些子空间的结构的讨论。
Let $\{T(t)\}_{t\geq0}$ be a $C_0$-semigroup on an infinite dimensional separable Hilbert space; a suitable definition of near $\{T(t)^*\}_{t\geq0}$ invariance of a subspace is presented in this paper. A series of prototypical examples for minimal nearly $\{S(t)^*\}_{t\geq0}$ invariant subspaces for the shift semigroup $\{S(t)\}_{t\geq0}$ on $L^2(0,\infty)$ are demonstrated, which have close links with nearly $T_θ^*$ invariance on Hardy spaces of the unit disk for Toeplitz operators associated with an inner function $θ$. Especially, the corresponding subspaces on Hardy spaces of the right half-plane and the unit disk are related to model spaces. This work further includes a discussion on the structure of the closure of certain subspaces related to model spaces in Hardy spaces.
