In this paper, we study the homogenous quotient modules of the Hardy module on the bidisk. The essential normality of the homogenous quotient modules is completely characterized. We also describe the essential spectru...In this paper, we study the homogenous quotient modules of the Hardy module on the bidisk. The essential normality of the homogenous quotient modules is completely characterized. We also describe the essential spectrum for a general quotient module. The paper also considers K-homology invariant defined in the case of the homogenous quotient modules on the bidisk.展开更多
In this paper, we characterize when the Toeplitz operator Tf and the Hankel operator Hg commute on the Hardy space of the bidisk. For certain types of bounded symbols f and g, we give a necessary and sufficient condit...In this paper, we characterize when the Toeplitz operator Tf and the Hankel operator Hg commute on the Hardy space of the bidisk. For certain types of bounded symbols f and g, we give a necessary and sufficient condition on the symbols to guarantee TfHg = HgTf.展开更多
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-Schm...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.展开更多
基金This work is partially supported by the National Natural Science Foundation of China(Grant No. 10525106)the Young Teacher Fund,the National Key Basic Research Project of China(Grant No. 2006CB805905)the Specialized Research for the Doctoral Program
文摘In this paper, we study the homogenous quotient modules of the Hardy module on the bidisk. The essential normality of the homogenous quotient modules is completely characterized. We also describe the essential spectrum for a general quotient module. The paper also considers K-homology invariant defined in the case of the homogenous quotient modules on the bidisk.
基金Supported by the National Natural Science Foundation of China (Grant Nos.10671028 10971020)
文摘In this paper, we characterize when the Toeplitz operator Tf and the Hankel operator Hg commute on the Hardy space of the bidisk. For certain types of bounded symbols f and g, we give a necessary and sufficient condition on the symbols to guarantee TfHg = HgTf.
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).
文摘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.
