On Certain Multivariable Subnormal Weighted Shifts and their Duals

Canadian mathematical bulletin

Ameer Athavale¹  Pramod Patil¹ 

[1] Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India

关键词: subnormal;    Reinhardt;    Betti numbers;   

DOI  :  10.4153/CMB-2011-188-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

To every subnormal $m$-variable weighted shift $S$ (with boundedpositive weights) corresponds a positive Reinhardt measure $mu$supported on a compact Reinhardt subset of $mathbb C^m$. We show that, for$m geq 2$, the dimensions of the $1$-st cohomology vector spacesassociated with the Koszul complexes of $S$ and its dual ${ilde S}$are different if a certain radial function happens to be integrablewith respect to $mu$ (which is indeed the case with many classicalexamples). In particular, $S$ cannot in that case be similar to${ilde S}$. We next prove that, for $m geq 2$, a Fredholm subnormal$m$-variable weighted shift $S$ cannot be similar to its dual.

【 授权许可】

Unknown