Essentially Reductive Hilbert Modules II
By Ronald G. Douglas. 2006
47 citations recorded by the source corpus.
Many Hilbert modules over the polynomial ring in m variables are essentially reductive, that is, have commutators which are compact. Arveson has raised the question of whether the closure of homogeneous ideals inherit this property and provided motivation to seek an affirmative answer. Positive results have been obtained by Arveson, Guo, Wang and the author. More recently, Guo and Wang extended the results to quasi-homogeneous ideals in two variables. Building on their techniques, in this note the author extends this result to Hilbert modules over certain Reinhardt domains such as ellipsoids in two variables and analyzes extending the result to the closure of quasi-homogeneous ideals in m variables when the zero variety has dimension one.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0ba66ab6076bc1ca92d51e0526b961f9282d6fdb
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In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- Quotients of standard Hilbert modules (2005, background): “Douglas [ Dou05a ] has generalized that result to the context of more general weighted shifts.”
- Essentially normal Hilbert modules and K-homology (2008, background): “erated by the identity operator and d-tuple {S1 ,..., Sd } .I f[I ] is essentially normal, then applying a result in [4, 16 ] here shows that the quotient submodule L 2(Bd )/[I ] also is, and hence one has a C ∗ -extension defined by”
- A new kind of index theorem (2005, methodology): “We consider the case of commuting weighted shifts using the notation of [ 16 ].”