2019/05/25 by Ameer Athavale, Athavale, Ameer · 1 citation
Mathematics · #Holomorphic and Operator Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.1905.10582
We record a lifting theorem for the intertwiner of two SΩ-isometries which are those subnormal operator tuples whose minimal normal extensions have their Taylor spectra contained in the Shilov boundary of a certain function algebra associated with Ω, Ω being a bounded convex domain in \Cn containing the origin. The theorem captures several known lifting results in the literature and yields interesting new examples of liftings as a consequence of its being applicabile to Cartesian products Ω of classical Cartan domains in \Cn. Further, we derive intrinsic characterizations of SΩ-isometries where Ω is a classical Cartan domain of any of the types I, II, III and IV, and we also provide a neat description of an SΩ-isometry in case Ω is a finite Cartesian product of such Cartan domains.