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arXiv · 2505.24325

Cartan Isometries and Toeplitz Operators on Cartan domains

Surjit Kumar·Milan Kumar Mal·Paramita Pramanick
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Abstract

We provide a description of the Shilov boundary of the classical Cartan domain in terms of Jordan triple determinant. As a consequence, we obtained an intrinsic characterization of Cartan isometries. Further, we obtain (i) invariance of Cartan isometries under the action of the biholomorphic automorphism group, and (ii) a Brown-Halmos type condition for Toeplitz operators on the Cartan domain. Also, we show that the zero operator is the only compact Toeplitz operator. Finally, we study the $\boldsymbol T$-Toeplitz operators and reflexivity of a Cartan isometry $\boldsymbol T.$

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Surjit Kumar, Milan Kumar Mal, Paramita Pramanick. 2025-05-30. Cartan Isometries and Toeplitz Operators on Cartan domains. https://arxiv.org/abs/2505.24325

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