Toeplitz Operators with Lagrangian Invariant Symbols Acting on the Poly-Fock Space of ℂn. (25th November 2021) - Arroyo Neri, Jorge Luis; Sánchez-Nungaray, Armando; Hernández Marroquin, Mauricio; López-Martínez, Raquiel R.
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.