On a relationship between orthogonal projections and Toeplitz operators on poly-Bergman spaces of the upper half-plane: vertical symbols

Maribel Loaiza; Miguel Antonio Morales-Ramos; María del Rosario Ramírez-Mora; Josué Ramírez-Ortega

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arXiv · 2604.26918

On a relationship between orthogonal projections and Toeplitz operators on poly-Bergman spaces of the upper half-plane: vertical symbols

Maribel Loaiza·Miguel Antonio Morales-Ramos·María del Rosario Ramírez-Mora·Josué Ramírez-Ortega

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Abstract

In the context of studying $C^*$-algebras generated by Toeplitz operators acting on the poly-Bergman space $\mathcal{A}^2_{n}(\Pi)$ of the upper half-plane $\Pi$, we introduce a system of all-but-one orthogonal projections in generic position. We show that the $C^*$-algebra generated by these orthoprojections is closely related to the $C^*$-algebra generated by all Toeplitz operators with vertical symbols satisfying boundary conditions. This result suggests a new approach in the study of Toeplitz operators acting on other reproducing kernel Hilbert spaces. Furthermore, the range of one of the orthoprojections herein has a reproducing kernel expressed in terms of the digamma and the Nielsen's beta functions. The harmonic function also emerges in this development.

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Maribel Loaiza, Miguel Antonio Morales-Ramos, María del Rosario Ramírez-Mora, Josué Ramírez-Ortega. 2026-04-29. On a relationship between orthogonal projections and Toeplitz operators on poly-Bergman spaces of the upper half-plane: vertical symbols. https://arxiv.org/abs/2604.26918

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