The biholomorphic invariance of essential normality on bounded symmetric domains
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929195233312768 |
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| author | Ding, Lijia |
| author_facet | Ding, Lijia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_05739 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The biholomorphic invariance of essential normality on bounded symmetric domains Ding, Lijia Functional Analysis Complex Variables Primary 46H25, Secondary 32B15, 32M15, 47A13 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. |
| title | The biholomorphic invariance of essential normality on bounded symmetric domains |
| topic | Functional Analysis Complex Variables Primary 46H25, Secondary 32B15, 32M15, 47A13 |
| url | https://arxiv.org/abs/2206.05739 |