$ C^* $-Algebra generated by $ n $-orthogonal projections and its relationship to Toeplitz operators acting on the poly-Fock space
Year: 2025
Type: article
Abstract: Starting from the system of orthogonal projections mapping the $ n $-poly-Fock space $ F_n^2(\mathbb{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(\mathbb{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(\mathbb{C}) $ with horizontal symbols having limit values at $ \pm \infty $. Our approach combines unitary equivalences induced by Bargmann-type transforms with a noncommutative Stone–Weierstrass-type argument to describe the algebras.
Source: AIMS Mathematics
Authors: Maribel Loaiza, Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Av. IPN 2508, 07360, CDMX, México, Miguel A. Morales-Ramos, María del Rosario Ramírez-Mora, Josué Ramírez-Ortega, NovaUniversitas, KM 34.5 Carretera Oaxaca-Puerto Ángel, Ocotlán de Morelos, Oaxaca, 71513, México, SECIHTI-Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Av. IPN 2508, 07360, CDMX, México, Facultad de Matemáticas, Universidad Veracruzana, Paseo 112, Lt. 2, Col. Nuevo Xalapa, Xalapa-Eqz, CP 91097, México
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,200
OpenAlex ID: W4415531715