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| Field | Value |
| Title | On Certain Multivariable Subnormal Weighted Shifts and their Duals |
| Names |
ATHAVALE, A
PATIL, P |
| Date Issued | 2013 (iso8601) |
| Abstract | For every subnormal m-variable weighted shift S (with bounded positive weights), there is a corresponding positive Reinhardt measure mu supported on a compact Reinhardt subset of C-m. We show that, for m >= 2, the dimensions of the 1-st cohomology vector spaces associated with the Koszul complexes of S and its dual (S) over tilde are different if a certain radial function happens to be integrable with respect to mu (which is indeed the case with many classical examples). In particular, S cannot in that case be similar to (S) over tilde. We next prove that, for m >= 2, a Fredholm subnormal m-variable weighted shift S cannot be similar to its dual. |
| Genre | Article |
| Topic | Subnormal |
| Identifier | CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 56(3)459-465 |