Cartan Isometries and Toeplitz Operators on Cartan domains

2025/05/30 by Surjit Kumar, Kumar, Surjit, Milan Kumar Mal +3 · 1 citation
Mathematics · #Holomorphic and Operator Theory #Algebraic and Geometric Analysis #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2505.24325

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.

Citations

• Toeplitz operators on the n-dimensional Hartogs triangle
• Brown-Halmos type Theorems on the proper images of bounded symmetric domains
• A note on Cartan isometries
• Some Exact Sequences for Toeplitz Algebras of Spherical Isometries

Cited by

• Brown-Halmos type characterization for the tetrablock

Related

• A note on Cartan isometries
• Radial-like Toeplitz operators on Cartan domains of type I
• Commuting Toeplitz operators and moment maps on Cartan domains of type III
• Radial Toeplitz operators on the weighted Bergman spaces of Cartan\n domains
• On certain Toeplitz operators and associated completely positive maps