arXiv 0807.39222008-07-24math.OAmath.FA

Essentially Reductive Weighted Shift Hilbert Modules

Ronald G. Douglas, Jaydeb Sarkar

备注：: 23 pages

英文摘要：

We discuss the relation between questions regarding the essential normality of finitely generated essentially spherical isometries and some results and conjectures of Arveson and Guo-Wang on the closure of homogeneous ideals in the m-shift space. We establish a general results for the case of two tuples and ideals with one dimensional zero variety. Further, we show how to reduce the analogous question for quasi-homogeneous ideals, to those results for homogeneous ones. Finally, we show that the essential reductivity of positive regular Hilbert modules is directly related to a generalization of the Arveson problem.

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