When Do Toeplitz and Hankel Operators Commute?
by
Rubén A. Martínez-Avendaño
University of Toronto

We completely classify all Toeplitz and Hankel operators which commute; namely, we prove that that a non-trivial Hankel operator and a non-trivial Toeplitz operator commute if and only if the Hankel operator has symbol z \psi, where \psi is the symbol of the Toeplitz operator, and \psi is an affine function of the characteristic function of certain ``anti-symmetric'' sets of the unit circle.

Date received: April 9, 1999