$\mathbb{C}^N$上的Fock空间上可逆加权复合算子的注记

A Note on Invertible Weighted Composition Operators on the Fock Space of $\mathbb{C}^N$

中文关键词:  Fock空间  加权复合算子  可逆  酉算子

英文关键词:Fock space  weighted composition operator  invertible  unitary

中文摘要:

      本文表明$\mathbb{C}^N$上的Fock空间上有界可逆加权复合算子是酉算子的非零常数倍,这是关于$\mathbb{C}^N$上的Fock空间上可逆加权复合算子已有刻画的一个补充,也是对$\mathbb{C}$上的Fock空间上相应结果的推广.

英文摘要:

      This paper shows that a bounded invertible weighted composition operator on the Fock space of $\mathbb{C}^N$ is nonzero multiples of a unitary operator, which is an addition to the recent result on invertible weighted composition operator on the Fock space of $\mathbb{C}^N$ and an extension to the corresponding result on the Fock space of $\mathbb{C}$.