Journal of the Ramanujan Mathematical Society

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Essentially Normal Hilbert Modules and K-Homology II:Quasi-homogeneous Hilbert Modules Over the Two Dimensional Unit Ball


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1 Department of Mathematics, Fudan University, Shanghai, 200433, China
     

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In this paper, we mainly consider quasi-homogeneous submodules of U-invariant analytic Hilbert modules over the two dimensional unit ball. It is shown that every quasi-homogeneous submodule M is essentially normal. This paper also shows that each quasi-homogeneous submodule of the Bergman module L2α(B2) is p-essentially normal for p > 2, and the same result also is valid for the Hardy module. The paper is associated with K-homology invariants arising from quasi-homogeneous quotient modules.
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  • Essentially Normal Hilbert Modules and K-Homology II:Quasi-homogeneous Hilbert Modules Over the Two Dimensional Unit Ball

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Authors

Kunyu Guo
Department of Mathematics, Fudan University, Shanghai, 200433, China
Kai Wang
Department of Mathematics, Fudan University, Shanghai, 200433, China

Abstract


In this paper, we mainly consider quasi-homogeneous submodules of U-invariant analytic Hilbert modules over the two dimensional unit ball. It is shown that every quasi-homogeneous submodule M is essentially normal. This paper also shows that each quasi-homogeneous submodule of the Bergman module L2α(B2) is p-essentially normal for p > 2, and the same result also is valid for the Hardy module. The paper is associated with K-homology invariants arising from quasi-homogeneous quotient modules.