Essentially Reductive Hilbert Modules
نویسنده
چکیده
Consider a Hilbert space obtained as the completion of the polynomials C[z ] 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 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.
منابع مشابه
Essentially Reductive Hilbert Modules II
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...
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