Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590232 | Journal of Functional Analysis | 2014 | 39 Pages |
Abstract
We extend the basic elements of Clark's theory of rank-one perturbations of backward shifts, to row-contractive operators associated to de Branges–Rovnyak type spaces H(b)H(b) contrastively contained in the Drury–Arveson space on the unit ball in CdCd. The Aleksandrov–Clark measures on the circle are replaced by a family of states on a certain noncommutative operator system, and the backward shift is replaced by a canonical solution to the Gleason problem in H(b)H(b). In addition we introduce the notion of a “quasi-extreme” multiplier of the Drury–Arveson space and use it to characterize those H(b)H(b) spaces that are invariant under multiplication by the coordinate functions.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Michael T. Jury,