Weighted composition operators on the Fock space  

作　　者：Kaikai Han Maofa Wang 

机构地区：[1]School of Mathematics and Statistics,Hebei University of Economics and Business,Shijiazhuang 050061,China [2]School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China

出　　处：《Science China Mathematics》2022年第1期111-126,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11771340)。

摘　　要：In this paper,we study weighted composition operators on theFock space F^(2).We prove that each bounded composition operator on F^(2) is complex symmetric.This is in sharp contrast with the phenomenon on the Hardy space H^(2)(D).We characterize Hermitian weighted composition operators and algebraic weighted composition operators with degree less than or equal to two on F^(2).In addition,we investigate cyclicity and hypercyclicity of complex symmetric weighted composition operators.We also characterize those weighted compositionoperators that preserveframes,tight frames or normalized tight frames on F^(2).Finally,we study mean ergodicity and uniformly mean ergodicity of weighted composition operators.

关 键 词：weighted composition operator Fock space complex symmetry CYCLICITY FRAME mean ergodicity 

分 类 号：O177[理学—数学]