Toeplitz Operators with Horizontal Symbols Acting on the Poly-Fock Spaces

摘要

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.