Toeplitz算子在Dirichlet空间上的亚正规性

Hyponormality of Toeplitz Operators on the Dirichlet Space

中文关键词:  Toeplitz算子  亚正规性  Dirichlet空间  调和Dirichlet空间.

英文关键词:Toeplitz operator  hyponormality  Dirichlet space  harmonic Dirichlet space.

中文摘要:

      本文中, 我们分别证明了符号函数$u$在Dirichlet空间上的投影是一个多项式时和$u$是一类特殊的调和函数时, Dirichlet空间上Toeplitz算子$T_u$是亚正规的充分必要条件是符号函数$u$是常值函数. 我们也证明了以调和多项式为符号的调和Dirichlet空间上Toeplitz算子是亚正规的当且仅当其符号函数是常值函数.

英文摘要:

      In this paper, we prove that the necessary and sufficient condition for a Toeplitz operator $T_u$ on the Dirichlet space to be hyponormal is that the symbol $u$ is constant for the case that the projection of $u$ in the Dirichlet space is a polynomial and for the case that $u$ is a class of special symbols, respectively. We also prove that a Toeplitz operator with harmonic polynomial symbol on the harmonic Dirichlet space is hyponormal if and only if its symbol is constant.