The Finite Sum of the Products of Two Toeplitz Operators

Abstract

We consider in this paper the question of when the finite sum of products of two Toeplitz operators is a finite-rank perturbation of a single Toeplitz operator on the Hardy space over the unit disk. A necessary condition is found. As a consequence we obtain a necessary and sufficient condition for the product of three Toeplitz operators to be a finite-rank perturbation of a single Toeplitz operator.2000 Mathematics subject classification: primary 47B35.

Finite rank sums of products of Toeplitz and Hankel operators

“…The corresponding problems on the Hardy space or Bergman space have been studied in [9][10][11][12] or [13].…”