Weighted Composition Operators That Preserve Frames On Weighted Hardy Spaces  

作　　者：Ya Li Dong Rui Liu Guo Xiang Lu 

机构地区：[1]School of Mathematical Sciences and LPMC,Nankai University,Tianjin,300071,P.R.China [2]School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan,430073,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第7期1645-1654,共10页数学学报（英文版）

基　　金：supported by Nation Natural Science Foundation of China(Grant Nos.11671214,11971348,12071230);MOE(Ministry of Education in China)Youth Foundation Project of Humanities and Social Sciences(Grant No.19YJCZH111)。

摘　　要：In this paper, we characterize weighted composition operators that preserve frames on the weighted Hardy spaces in the unit disk. In particular, we obtain the symbol properties of the bounded invertible weighted composition operators. Moreover, we establish the equivalence between bounded invertible operators and frame-preserving operators. Furthermore, we show that weighted composition operator preserves frames if and only if it preserves the Riesz bases property. Additionally,we investigate the weighted composition operators that preserve tight or normalized tight frames on the Dirichlet space.

关 键 词：Weighted composition operators Weighted Hardy spaces FRAMES invertible 

分 类 号：O177[理学—数学]