Toeplitz Operators with Lagrangian Invariant Symbols Acting on the Poly-Fock Space of ℂn. (25th November 2021)

• Record Type: Journal Article
• Authors: Arroyo Neri, Jorge Luis; Sánchez-Nungaray, Armando; Hernández Marroquin, Mauricio; López-Martínez, Raquiel R.
• Other Names: Rafeiro Humberto Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-11-25
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/9919243
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : We introduce the so-called extended Lagrangian symbols, and we prove that the C ∗ -algebra generated by Toeplitz operators with these kind of symbols acting on the homogeneously poly-Fock space of the complex space ℂ n is isomorphic and isometric to the C ∗ -algebra of matrix-valued functions on a certain compactification of ℝ n obtained by adding a sphere at the infinity; moreover, the matrix values at the infinity points are equal to some scalar multiples of the identity matrix.