Clark theory in the Drury-Arveson space

详细信息    查看全文

• 作者：Michael T. Jury
• 关键词：Aleksandrov&ndash ; Clark measure ; Row contraction ; de Branges&ndash ; Rovnyak space ; Gleason problem
• 刊名：Journal of Functional Analysis
• 出版年：15 March, 2014
• 年：2014
• 卷：266
• 期：6
• 页码：3855-3893
• 全文大小：422 K

文摘

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 contrastively contained in the Drury-Arveson space on the unit ball in . 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 . In addition we introduce the notion of a 鈥渜uasi-extreme鈥?multiplier of the Drury-Arveson space and use it to characterize those spaces that are invariant under multiplication by the coordinate functions.