The biholomorphic invariance of essential normality on bounded symmetric domains

Ding, Lijia

doi:10.1090/tran/9167

The biholomorphic invariance of essential normality on bounded symmetric domains
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by Lijia Ding;

Trans. Amer. Math. Soc. 377 (2024), 4993-5026

DOI: https://doi.org/10.1090/tran/9167

Published electronically: May 21, 2024

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Abstract:

This paper mainly concerns the biholomorphic invariance of $p$-essential normality of Hilbert modules on bounded symmetric domains. By establishing new integral formulas concerning rational function kernels for the Taylor functional calculus, we prove a biholomorphic invariance result related to the $p$-essential normality. Furthermore, for quotient analytic Hilbert submodules determined by analytic varieties, we develop an algebraic approach to proving that the $p$-essential normality is preserved invariant if the coordinate multipliers are replaced by arbitrary automorphism multipliers. Moreover, the Taylor spectrum of the compression tuple is calculated under a mild condition, which gives a solvability result of the corona problem for quotient submodules. As applications, we extend the recent results on the equivalence between $\infty$-essential normality and hyperrigidity.

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