Essentially Reductive Weighted Shift Hilbert Modules

Abstract

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.

23 pages

References in corpus (3)

• p-Summable Commutators in Dimension d
• Essentially Reductive Hilbert Modules II
• The curvature invariant of a Hilbert module over C[z_1,...,z_d]

Cited by in corpus (6)

• A harmonic analysis approach to essential normality of principal submodules
• Essential normality and the decomposability of algebraic varieties
• Spherical Tuples of Hilbert Space Operators
• Geometric Arveson-Douglas Conjecture and Holomorphic Extension
• Geometirc Arveson-Douglas Conjecture - Decomposition of Varieties
• Stable division and essential normality: the non-homogeneous and quasi homogeneous cases