 

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. 


Abstract
We record a lifting theorem for the intertwiner of two S_{Ω}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 C^{n} 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 C^{n}. Further, we derive intrinsic characterizations of S_{Ω}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 S_{Ω}isometry in case Ω is a finite Cartesian product of such Cartan domains. 

Acknowledgements
N/A


Author information
Ameer Athavale:
Department of Mathematics
Indian Institute of Technology Bombay
Powai, Mumbai 400076, India
athavale@math.iitb.ac.in

