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On Certain Multivariable Subnormal Weighted Shifts and their Duals

DSpace at IIT Bombay

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Field Value
 
Title On Certain Multivariable Subnormal Weighted Shifts and their Duals
 
Creator ATHAVALE, A
PATIL, P
 
Subject subnormal
Reinhardt
Betti numbers
TUPLES
FREDHOLM
 
Description 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.
 
Publisher CANADIAN MATHEMATICAL SOC
 
Date 2014-10-17T05:29:50Z
2014-10-17T05:29:50Z
2013
 
Type Article
 
Identifier CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 56(3)459-465
http://dx.doi.org/10.4153/CMB-2011-188-x
http://dspace.library.iitb.ac.in/jspui/handle/100/16070
 
Language en