The Poisson Kernel for Hardy Algebras |
| |
Authors: | Paul S. Muhly Baruch Solel |
| |
Affiliation: | (1) Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA;(2) Department of Mathematics, Technion, 32000 Haifa, Israel |
| |
Abstract: | This note contributes to a circle of ideas that we have been developing recently in which we view certain abstract operator algebras H∞(E), which we call Hardy algebras, and which are noncommutative generalizations of classical H∞, as spaces of functions defined on their spaces of representations. We define a generalization of the Poisson kernel, which “reproduces” the values, on , of the “functions” coming from H∞(E). We present results that are natural generalizations of the Poisson integral formula. They also are easily seen to be generalizations of formulas that Popescu developed. We relate our Poisson kernel to the idea of a characteristic operator function and show how the Poisson kernel identifies the “model space” for the canonical model that can be attached to a point in the disc . We also connect our Poisson kernel to various “point evaluations” and to the idea of curvature. The first named author was supported in part by grants from the National Science Foundation and from the U.S.-Israel Binational Science Foundation. The second named author was supported in part by the U.S.-Israel Binational Science Foundation and by the B. and G. Greenberg Research Fund (Ottawa). |
| |
Keywords: | KeywordHeading" >Mathematics Subject Classification (2000). 47L55 46L08 46L52 47L30 |
本文献已被 SpringerLink 等数据库收录! |
|