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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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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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