New York Journal of Mathematics
Volume 25 (2019), 934-948


Ameer Athavale

A note on Cartan isometries

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Published: September 20, 2019.
Keywords: Cartan domain, Cartan isometry, spherical isometry, subnormal.
Subject: Primary 47A13, 47B20.

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.



Author information

Ameer Athavale:
Department of Mathematics
Indian Institute of Technology Bombay
Powai, Mumbai 400076, India