Adjoints of slant Toeplitz operators

In this paper, we will use the Birkhoff's ergodic theorem to do some finer analysis on the spectral properties of slant Toeplitz operators. For example, we will show that if phi is an invertible L-infinity function on the unit circle, then almost every point in sigma(A(phi)*) is not an eigenvalue of A(phi)*. More specifically, we will show that the point spectrum of A(phi)* is contained in a circle with positive radius.