论文标题
polydisk上的耐力空间上的通用toeplitz操作员
Universal Toeplitz operators on the Hardy space over the polydisk
论文作者
论文摘要
Hilbert Space的不变子空间问题（ISP）询问每个有限的线性运算符是否具有非平凡的封闭不变子空间。由于存在通用操作员（从ROTA的意义上），可以通过仅描述这些操作员的不变子空间来解决ISP。 We characterize all anaytic Toeplitz operators $T_ϕ$ on the Hardy space $H^2(\mathbb{D}^n)$ over the polydisk $\mathbb{D}^n$ for $n>1$ whose adjoints satisfy the Caradus criterion for universality, that is, when $T_ϕ^*$ is surjective and has infinite dimensional kernel.特别是，如果$ \ mathbb {d}^n $在非稳定内部功能中的$ ϕ $，或ring $ \ mathbb {c} [z__1，\ ldots，z_n] $中的zeros中的zeros in $ \ mathbb {d}^n $ in $ n $ n $ the $对于$ h^2（\ mathbb {d}^n）$是通用的。这些结果的类似物以$ n = 1 $不正确。
The Invariant Subspace Problem (ISP) for Hilbert spaces asks if every bounded linear operator has a non-trivial closed invariant subspace. Due to the existence of universal operators (in the sense of Rota), the ISP may be solved by describing the invariant subspaces of these operators alone. We characterize all anaytic Toeplitz operators $T_ϕ$ on the Hardy space $H^2(\mathbb{D}^n)$ over the polydisk $\mathbb{D}^n$ for $n>1$ whose adjoints satisfy the Caradus criterion for universality, that is, when $T_ϕ^*$ is surjective and has infinite dimensional kernel. In particular if $ϕ$ in a non-constant inner function on $\mathbb{D}^n$, or a polynomial in the ring $\mathbb{C}[z_1,\ldots,z_n]$ that has zeros in $\mathbb{D}^n$ but is zero-free on $\mathbb{T}^n$, then $T_ϕ^*$ is universal for $H^2(\mathbb{D}^n)$. The analogs of these results for $n=1$ are not true.
