Essentially normal Hilbert modules and \(K\)-homology. IV: Quasi-homogenous quotient modules of Hardy module on the polydisks
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.
scientific article; zbMATH DE number 6131118
scientific article