Toeplitz Operators with Horizontal Symbols Acting on the Poly-Fock Spaces - Armando Sánchez-Nungaray; Carlos González-Flores; Raquiel Rufino López-Martínez; Jorge Luis Arroyo-Neri (Journal of Function Spaces)
We describe the C⁎-algebra generated by the Toeplitz operators acting on each poly-Fock space of the complex plane C with the Gaussian measure, where the symbols are bounded functions depending only on x=Re  z and have limit values at y=-∞ and y=∞. The C⁎ algebra generated with this kind of symbols is isomorphic to the C⁎-algebra functions on extended reals with values on the matrices of dimension n×n, and the limits at y=-∞ and y=∞ are scalar multiples of the identity matrix.