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Essential Normality for Beurling-Type Quotient Modules over Tube-Type Domains

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In this note we investigate the essential normality of the Beurling-type quotient module \({\mathcal {D}}:=H^2(\Omega )\ominus \eta H^2(\Omega )\) with an inner function \(\eta \) inside \(A(\Omega )\) over an irreducible tube-type domain \(\Omega \). For the Lie ball (of rank 2), we characterize the essential normality of the corresponding quotient Hardy module and determine its essential spectrum. For domains of higher rank, we introduce the analogous concept of k-normality and again characterize \((r-1)\)-normality in terms of representation theory of the maximal compact subgroup.

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  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Shuyi Zhang

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  1. Shuyi Zhang
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Correspondence to Shuyi Zhang.

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This work was partially supported by grants NSFC 11722102 and LMNS, Fudan. The author thanks Prof. H. Upmeier for valuable discussions and Prof. K. Wang for many useful suggestions.

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Zhang, S. Essential Normality for Beurling-Type Quotient Modules over Tube-Type Domains. Integr. Equ. Oper. Theory 93, 3 (2021). https://doi.org/10.1007/s00020-020-02613-5

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  • DOI: https://doi.org/10.1007/s00020-020-02613-5

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