Geodesic
On Certain Multivariable Subnormal Weighted Shifts and their Duals
Canadian mathematical bulletin, Tome 56 (2013) no. 3, pp. 459-465

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DOI

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 ${{\mathbb{C}}^{m}}$ . We show that, for $m\,\ge \,2$ , the dimensions of the 1-st cohomology vector spaces associated with the Koszul complexes of $S$ and its dual $\widetilde{S}$ are different if a certain radial function happens to be integrable with respect to μ (which is indeed the case with many classical examples). In particular, $S$ cannot in that case be similar to $\widetilde{S}$ . We next prove that, for $m\,\ge \,2$ , a Fredholm subnormal $m$ -variable weighted shift $S$ cannot be similar to its dual.
DOI : 10.4153/CMB-2011-188-x
Mots-clés : 47B20, subnormal, Reinhardt, Betti numbers 
Athavale, Ameer; Patil, Pramod. On Certain Multivariable Subnormal Weighted Shifts and their Duals. Canadian mathematical bulletin, Tome 56 (2013) no. 3, pp. 459-465. doi: 10.4153/CMB-2011-188-x
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     title = {On {Certain} {Multivariable} {Subnormal} {Weighted} {Shifts} and their {Duals}},
     journal = {Canadian mathematical bulletin},
     pages = {459--465},
     year = {2013},
     volume = {56},
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     doi = {10.4153/CMB-2011-188-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-188-x/}
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