Free holomorphic functions and operator model theory

2011/11/22 by Popescu, Gelu
#46L07 #46L52 #46T25 #47A20 #47A45 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1111.5282

Abstract

This paper is an attempt to find large classes of noncommutative multivariable functions g:Ω⊂ [B(\cH)ⁿ]₁^-→ B(\cH)ⁿ for which a reasonable operator model theory and dilation theory can be developed for the noncommutative domain g(Ω). In other words, we want to transfer the free analogue of Nagy-Foias theory from the unit ball [B(\cH)ⁿ]₁ to other noncommutative domains, using appropriate maps.

Related

• Free biholomorphic functions and operator model theory,II
• Noncommutative domains, universal operator models, and operator algebras, II
• Operator theory on noncommutative domains
• Foundations of Free Noncommutative Function Theory
• Noncommutative Berezin transforms and model theory