Toeplitz operators with Lagrangian invariant symbols acting on the poly-Fock space of \(\mathbb{C}^n\) (Q2064453)

Summary: We introduce the so-called extended Lagrangian symbols, and we prove that the \(C^\ast\)-algebra generated by Toeplitz operators with these kind of symbols acting on the homogeneously poly-Fock space of the complex space \(\mathbb{C}^n\) is isomorphic and isometric to the \(C^\ast\)-algebra of matrix-valued functions on a certain compactification of \(\mathbb{R}^n\) 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.