Journal article
The Poisson Kernel for Hardy Algebras
Complex analysis and operator theory, Vol.3(1), pp.221-242
03/2009
DOI: 10.1007/s11785-008-0047-0
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
$${\mathbb{D}}((E^{\sigma})^*)$$
, 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
$${\mathbb{D}}((E^{\sigma})^*)$$
. We also connect our Poisson kernel to various “point evaluations” and to the idea of curvature.
Details
- Title: Subtitle
- The Poisson Kernel for Hardy Algebras
- Creators
- Paul Muhly - Department of MathematicsUniversity of IowaIowa CityIA52242USABaruch Solel - Department of MathematicsTechnion32000HaifaIsrael
- Resource Type
- Journal article
- Publication Details
- Complex analysis and operator theory, Vol.3(1), pp.221-242
- Publisher
- Birkhäuser-Verlag
- DOI
- 10.1007/s11785-008-0047-0
- ISSN
- 1661-8254
- eISSN
- 1661-8262
- Language
- English
- Date published
- 03/2009
- Academic Unit
- Mathematics; Statistics and Actuarial Science
- Record Identifier
- 9984083805302771
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