کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4590869 | 1334991 | 2011 | 26 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: A harmonic analysis approach to essential normality of principal submodules A harmonic analysis approach to essential normality of principal submodules](/preview/png/4590869.png)
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.
Journal: Journal of Functional Analysis - Volume 261, Issue 11, 1 December 2011, Pages 3155-3180