Essentially normal Hilbert modules and \(K\)-homology. IV: Quasi-homogenous quotient modules of Hardy module on the polydisks
type: Item
instance of: scholarly article
title: Essentially normal Hilbert modules and \(K\)-homology. IV: Quasi-homogenous quotient modules of Hardy module on the polydisks
zbMATH Open document ID: 1267.47011
author: Kunyu Guo
author: Penghui Wang
published in: Science China. Mathematics
publication date: 2013-01-28T00:00:00Z
review text: In Part III of this series [\textit{K.-Y. Guo} and \textit{P.-H. Wang}, Sci. China, Ser. A 50, No. 3, 387--411 (2007; Zbl 1121.47002)], the authors presented a complete characterization of the essential normality of homogenous quotient modules of the Hardy modules \(H^2(\mathbb{D}^d)\) when \(d = 2\). The paper under review is a continuation of the above mentioned paper when \(d \geq 3\). The authors give a complete characterization for the essential normality of quasi-homogenous quotient modules of \(H^2(\mathbb{D}^d)\). They show that, if \(d \geq 3\), then all the principle homogenous quotient modules of \(H^2(\mathbb{D}^d)\) are not essentially normal. Parts I and II have appeared in [Math. Ann. 340, No.~4, 907--934 (2008; Zbl 1148.47005)] and [J. Ramanujan Math. Soc. 22, No.~3, 259--281 (2007; Zbl 1148.47006)], respectively.
reviewed by: Mohammad Sal Moslehian
Mathematics Subject Classification ID: 47A13
Mathematics Subject Classification ID: 47A20
Mathematics Subject Classification ID: 46C99
Mathematics Subject Classification ID: 46H25
zbMATH DE Number: 6131118
zbMATH Keywords: essential normality
zbMATH Keywords: Hilbert modules
zbMATH Keywords: polydisk
zbMATH Keywords: quotient modules
zbMATH Keywords: quasi-homogenous polynomial
MaRDI profile type: Publication
full work available at URL: s11425-012-4395-x
OpenAlex ID: W2263815122
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DOI: 10.1007/S11425-012-4395-X
description: scientific article; zbMATH DE number 6131118