Hilbert-Schmidtness of Submodules in H^(2)(D^(2))Containing(z)-β(w)  

作　　者：Chao Zu Yixin Yang Yufeng Lu 

机构地区：[1]Department of Mathematical Sciences,Dalian University of Technology,Dalian,Liaoning 116024,P.R.China

出　　处：《Communications in Mathematical Research》2023年第3期331-341,共11页数学研究通讯（英文版）

基　　金：supported by the National Nature Science Foundation of China (Grant Nos.12031002,11971086);supported by the Dalian High-Level Talent Innovation Project (Grant No.2020RD09).

摘　　要：A closed subspace M of the Hardy space H^(2)(D^(2))over the bidisk is called submodule if it is invariant under multiplication by coordinate functions z and w.Whether every finitely generated submodule is Hilbert-Schmidt is an unsolved problem.This paper proves that every finitely generated submodule M containing(z)-Φ(w)is Hilbert-Schmidt,where 0(z),p(w)are two finite Blaschke products.

关 键 词：Hardy space over the bidisk Hilbert-Schmidt submodule fringe operator Fredholm index 

分 类 号：O175[理学—数学]