论文标题
CESàRO操作员的见解：Shift Semigroups和不变子空间
Insights on the Cesàro operator: shift semigroups and invariant subspaces
论文作者
论文摘要
当CESàRO运算符$ \ MATHCAL {C} $下的封闭子空间在经典的耐强度空间上$ h^2（\ Mathbb d）$时，并且仅当其正交补充是在$ C_0 $ -Semoggon of Admogonal the Admogonal的构图运算符下不变的。 $ t \ geq 0 $和$ z \ in \ mathbb d $的e^{ - t} $。相应的结果也包含在hardy空间$ h^p（\ mathbb d）$的$ 1 <p <\ infty $。此外，在希尔伯特（Hilbert）空间环境中，通过将$ \ Mathcal {c} $的不变子空间链接到封闭的标准右移半群的封闭不变子空间的晶格，该子空间是在特定的加权$ l^2 $ - 空间上的，我们在线上展示了一大批非整体封闭式的范围，并提供了一个特定的范围，并在特定的范围内提供了一个完整的范围，以实现完整的形式，以实现完整的形式，以下完整的特征，描述$ \ Mathcal {C} $的所有不变子空间的晶格的方法的限制。最后，我们提出了一个功能性演算参数，该参数使我们能够扩展Mashreghi，Ptak和Ross关于$ \ Mathcal {C} $的平方根的最新结果，并讨论其不变子空间。
A closed subspace is invariant under the Cesàro operator $\mathcal{C}$ on the classical Hardy space $H^2(\mathbb D)$ if and only if its orthogonal complement is invariant under the $C_0$-semigroup of composition operators induced by the affine maps $φ_t(z)= e^{-t}z + 1 - e^{-t}$ for $t\geq 0$ and $z\in \mathbb D$. The corresponding result also holds in the Hardy spaces $H^p(\mathbb D)$ for $1<p<\infty$. Moreover, in the Hilbert space setting, by linking the invariant subspaces of $\mathcal{C}$ to the lattice of the closed invariant subspaces of the standard right-shift semigroup acting on a particular weighted $L^2$-space on the line, we exhibit a large class of non-trivial closed invariant subspaces and provide a complete characterization of the finite codimensional ones, establishing, in particular, the limits of such an approach towards describing the lattice of all invariant subspaces of $\mathcal{C}$. Finally, we present a functional calculus argument which allows us to extend a recent result by Mashreghi, Ptak and Ross regarding the square root of $\mathcal{C}$, and discuss its invariant subspaces.
