2004/04/07 by Ronald G. Douglas, Douglas, Ronald G.
Mathematics · #47B99 #47L15 #47L80 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.FA #math.OA #msc:47B99 #msc:47L15 #msc:47L80
paper · pdf · doi:10.48550/arxiv.math/0404167
17 pages; revision adds arguments for cross-commutator; to appear in Journal of Operator Theory
openalex publication_date 2004/04/07 · arxiv created 2004/05/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a Hilbert space obtained as the completion of the polynomials C[z in m-variables for which the mnonomials 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 Hm2. 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.