@article{Loaiza2025, 
author = {Maribel Loaiza and Miguel A. Morales-Ramos and María del Rosario Ramírez-Mora and Josué Ramírez-Ortega},
title = {C    ∗  -Algebra generated by    n-orthogonal projections and its relationship to Toeplitz operators acting on the poly-Fock space},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {10},
pages = {24352-24370},
keywords = {Toeplitz operator, orthogonal projection, C∗-algebra, Fock space, polyanalytic function},
url = {https://www.sciopen.com/article/10.3934/math.20251080},
doi = {10.3934/math.20251080},
abstract = {Starting from the system of orthogonal projections mapping the    n-poly-Fock space        F    n    2    (      C    ) onto the true-poly-Fock components, we constructed a system of all-but-one orthogonal projections in generic position. We described the        C    ∗  -algebra generated by these projections via an isomorphism with a subalgebra of matrix-valued continuous functions on the two-point compactification of the real line. In addition, we studied the        C    ∗  -algebra generated by a Toeplitz operator with a horizontal symbol and the orthogonal projections from        F    n    2    (      C    ) onto the true-poly-Fock subspaces. An interesting fact in this work was that the        C    ∗  -algebras studied herein contain the        C    ∗  -algebra generated by all Toeplitz operators acting on        F    n    2    (      C    ) with horizontal symbols having limit values at    ±  ∞. Our approach combines unitary equivalences induced by Bargmann-type transforms with a noncommutative Stone–Weierstrass-type argument to describe the algebras.}
}