Quadratic Hyponormality and 2-Hyponormality for Toeplitz Operators

Abstract.

In this note we prove the conjecture given in [11]: Let 0 < α < 1 and let ψ be the conformal map of the unit disk onto the interior of the ellipse with vertices ±(1+α)i and passing through ±(1−α). If $\varphi = \psi + \lambda \overline \psi$ then T _φ is quadratically hyponormal if and only if T _φ is 2–hyponormal.