加权Fock空间上对偶Toeplitz算子的紧性  

The compactness of dual Toeplitz operators on weighted Fock spaces

作　　者：李然 张成佳 孙铭浩 LI Ran;ZHANG Chengjia;SUN Minghao(School of Mathematics,Liaoning Normal University,Dalian 116081,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116081

出　　处：《辽宁师范大学学报(自然科学版)》2025年第1期80-85,共6页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11901269);辽宁省教育厅基本科研项目(JYTMS20231041)。

摘　　要：在加权有限维Fock空间的研究框架下,通过构造一族与该空间特性相适应的函数,系统地讨论了具有反全纯符号的Hankel算子在该空间中的有界性与紧性问题.首先严格给出了Hankel算子有界和紧的充要条件,从而为刻画此类算子在加权有限维Fock空间中的行为提供了清晰的理论准则.在此基础上,进一步深入探究了Hankel算子与Toeplitz算子及其对偶Toeplitz算子之间的深层关联和相互影响.通过分析这些关系,得到了对偶Toeplitz算子在加权有限维Fock空间上的紧性条件,为理解这类算子提供了新的视角与工具.这些研究成果不仅丰富和完善了对Fock空间中运算子理论的认识,也为后续相关领域的研究提供了有益的参考与启示.Within the research framework of weighted finite-dimensional Fock spaces,by constructing a family of functions suited to the characteristics of these spaces,this work systematically discusses the boundedness and compactness of Hankel operators with anti-holomorphic symbols.First,we rigorously present the necessary and sufficient conditions for the boundedness and compactness of Hankel operators,thereby offering clear theoretical criteria for characterizing the behavior of such operators in weighted finite-dimensional Fock spaces.On this basis,we further delve into the deep connections and mutual influences among Hankel operators,Toeplitz operators,and dual Toeplitz operators.By examining these relationships,we derive the conditions for the compactness of dual Toeplitz operators in weighted finite-dimensional Fock spaces,providing new perspectives and tools for understanding these operators.These findings not only enrich and enhance our comprehension of operator theory in Fock spaces but also offer valuable insights and references for subsequent research in related fields.

关 键 词：FOCK空间 对偶TOEPLITZ算子 紧性 

分 类 号：O177.1[理学—数学]