arXiv subjects

Josué Ramírez-Ortega

Publications and source records attributed to Josué Ramírez-Ortega.

3 recordsLinked to original sources

arXiv2026

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

In the context of studying $C^*$-algebras generated by Toeplitz operators acting on the poly-Bergman space $\mathcal{A}^2_{n}(Π)$ of the upper half-plane $Π$, 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.

math.OA↗

arXiv2023

Toeplitz Operators Acting on True-Poly-Bergman Type Spaces of the Two-Dimensional Siegel Domain: Nilpotent Symbols

We describe certain $C^*$-algebras generated by Toeplitz operators with nilpotent symbols and acting on a poly-Bergman type space of the Siegel domain $D_{2} \subset \mathbb{C}^{2}$. Bounded measurable functions of the form $c(\text{Im}\, ζ_{1}, \text{Im}\, ζ_{2} - |ζ_1|^{2})$ are called nilpotent symbols. In this work we consider symbols of the form $a(\text{Im}\, ζ_1) b(\text{Im}\, ζ_2 -|ζ_1|^{2})$, where both limits $\lim\limits_{s\rightarrow 0^+} b(s)$ and $\lim\limits_{s\rightarrow +\infty} b(s)$ exist, and $a(s)$ belongs to the set of piece-wise continuous functions on $\overline{\mathbb{R}}=[-\infty,+\infty]$ and having one-side limit values at each point of a finite set $D\subset \mathbb{R}$. We prove that the $C^*$-algebra generated by all Toeplitz operators $T_{ab}$ is isomorphic to $C(\overlineΠ)$, where $\overlineΠ=\overline{\mathbb{R}} \times \overline{\mathbb{R}}_+$ and $\overline{\mathbb{R}}_+=[0,+\infty]$.

math.OA↗

arXiv2023

Toeplitz Operators on Two Poly-Bergman-Type Spaces of the Siegel Domain $D_2 \subset \mathbb{C}^2$ with Continuous Nilpotent Symbols

We describe certain $C^*$-algebras generated by Toeplitz operators with nilpotent symbols and acting on a poly-Bergman type space of the Siegel domain $D_{2} \subset \mathbb{C}^{2}$. Bounded measurable functions of the form $\tilde{c}(ζ) = c(\text{Im}\, ζ_{1}, \text{Im}\, ζ_{2} - |ζ_1|^{2})$ are called nilpotent symbols. In this work we consider symbols of the form $\tilde{a}(ζ) = a(\text{Im}\, ζ_1)$ and $\tilde{b}(ζ) = b(\text{Im}\, ζ_2 -|ζ_1|^{2})$, where both limits $\lim\limits_{s\rightarrow 0^+} b(s)$ and $\lim\limits_{s\rightarrow +\infty} b(s)$ exist, and $a$ belongs to the set of piece-wise continuous functions on $\overline{\mathbb{R}}=[-\infty,+\infty]$ and with one-sided limits at $0$. We describe certain $C^*$-algebras generated by such Toeplitz operators that turn out to be isomorphic to subalgebras of $M_n(\mathbb{C}) \otimes C(\overlineΠ)$, where $\overlineΠ=\overline{\mathbb{R}} \times \overline{\mathbb{R}}_+$ and $\overline{\mathbb{R}}_+=[0,+\infty]$.

math.OA↗