The paper characterizes Cartan isometries and Toeplitz operators on all classical Cartan domains by simple equations involving the Jordan triple determinant.
Arazy,A survey of invariant Hilbert spaces of analytic functions on bounded symmetric domains, Contemporary Mathematics,185(1995), 7-65
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Cartan Isometries and Toeplitz Operators on Cartan domains
The paper characterizes Cartan isometries and Toeplitz operators on all classical Cartan domains by simple equations involving the Jordan triple determinant.