Analytic functionals for the non-commutative disc algebra
نویسندگان
چکیده
The main objects of study in this paper are those functionals that analytic the sense they annihilate non-commutative disc algebra. In classical univariate case, a theorem F. and M. Riesz implies such must be given as integration against an absolutely continuous measure on circle. We develop generalizations result to multivariate setting, upon reinterpreting result. one direction, we show GNS representation naturally associated functional Cuntz algebra cannot have any singular summand. Following different interpretation, seek weak-⁎ extensions free operator system. contrast with do not always exist, identify obstruction precisely terms so-called universal structure projection. also apply our ideas commutative algebras multipliers some complete Nevanlinna–Pick function spaces.
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2022
ISSN: ['0022-1236', '1096-0783']
DOI: https://doi.org/10.1016/j.jfa.2021.109306