A harmonic analysis approach to essential normality of principal submodules
By Ronald G. Douglas, Kai Wang. 2011
47 citations recorded by the source corpus.
Guo and the second author have shown that the closure [I] in the Drury–Arveson space of a homogeneous principal ideal I in C[z1,…,zn] is essentially normal. In this note, the authors extend this result to the closure of any principal polynomial ideal in the Bergman space. In particular, the commutators and cross-commutators of the restrictions of the multiplication operators are shown to be in the Schatten p-class for p>n. The same is true for modules generated by polynomials with vector-valued coefficients. Further, the maximal ideal space XI of the resulting C⁎-algebra for the quotient module is shown to be contained in Z(I)∩∂Bn, where Z(I) is the zero variety for I, and to contain all points in ∂Bn that are limit points of Z(I)∩Bn. Finally, the techniques introduced enable one to study a certain class of weight Bergman spaces on the ball.
Subfields: Algebra and Number Theory, Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/b2c9c170659e7f0b5ef8472d60d909145a7a48c1
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In Algebra and Number Theory
In Applied Mathematics
Citations in the corpus
- Operator Theory and Function Theory in Drury–Arveson Space and Its Quotients (2013, background): “There is reason to believe that the conclusion is true also for the case where L is generated by K-valued polynomials, indeed some positive results have been obtained for quasi-homogeneous submodules [56, 75, 76] or in the case of principal submodules [57, 66, 76].”