Essentially Reductive Hilbert Modules

Details Essentially Reductive Hilbert Modules Essentially Reductive Hilbert Modules

2004-04-07

arxiv.org/abs/math/0404167v2

Mathematics

Operator Algebras

17 pages; revision adds arguments for cross-commutator; to appear in Journal of Operator Theory

Scientific paper

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 H_m^2. 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.

Affiliated with

Also associated with

No associations

Rating

Essentially Reductive Hilbert Modules does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Essentially Reductive Hilbert Modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Essentially Reductive Hilbert Modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-244087