Essentially Reductive Hilbert Modules
By Ronald G. Douglas. 2004
60 citations recorded by the source corpus.
Consider a Hilbert space obtained as the completion of the polynomials C [ zzz ] in m -variables for which the monomials are orthogonal. If the commuting weighted shifts defined by the coordinate functions are essentially normal, then the same is true for their restrictions to invariant subspaces spanned by monomials. This generalizes the result of Arveson [4] in which the Hilbert space is the m -shift Hardy space H 2 m . He establishes his result for the case of finite multiplicity and shows the self-commutators lie in the Schatten p -class for p > m . We establish our result at the same level of generality. We also discuss the K -homology invariant defined in these cases.
Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/20bbfa6ebac0e351fe40028f667201fc2a9139af
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In Algebra and Number Theory
In Applied Mathematics
- Michael Hartz
- Kai Wang
- Orr Shalit
- Ronald G. Douglas
- Joerg Eschmeier
- Miroslav Englis
- Kunyu Guo
- Raphael Clouatre
In Mathematical Physics
Citations in the corpus
- Operator Theory and Function Theory in Drury–Arveson Space and Its Quotients (2013, background): “The first item is proved in [23, 52] and the last one is proved in [81]; the rest are proved in [74].”
- Essentially Reductive Hilbert Modules II (2006, methodology): “We recall a lemma from [2] and [10] which is one starting point for Guo and Wang [17].”
- A harmonic analysis approach to essential normality of principal submodules (2011, background): “1 in [18] or the related result in [3,11,16,17], it follows that all the operators Qf are essentially normal, or [Qf ,Q∗g] ∈ K(Qp) for f,g ∈ C[z1, .”