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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.24325 |
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| _version_ | 1866908385276854272 |
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| author | Kumar, Surjit Mal, Milan Kumar Pramanick, Paramita |
| author_facet | Kumar, Surjit Mal, Milan Kumar Pramanick, Paramita |
| contents | 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 $\boldsymbol T.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_24325 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cartan Isometries and Toeplitz Operators on Cartan domains Kumar, Surjit Mal, Milan Kumar Pramanick, Paramita Functional Analysis Primary 47A13, 47B32, 47B35, Secondary 32M15 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 $\boldsymbol T.$ |
| title | Cartan Isometries and Toeplitz Operators on Cartan domains |
| topic | Functional Analysis Primary 47A13, 47B32, 47B35, Secondary 32M15 |
| url | https://arxiv.org/abs/2505.24325 |