TOEPLITZ OPERATORS WITH BOUNDED HARMONIC SYMBOLS.

In this paper we have shown that if φ ∈ h∞(D) and T(α)φ is the Toeplitz operator with symbol φ defined on the weighted Bergman space L²a(dAα) and if the set {(T(α)φ)*T(α)φ f,(T(α)φ)* f, T(α)f,f} fois linearly dependent for all f ∈ L2a(dAα) then either φ is a constant function or there exists λα, µα ∈ C such that φ-µα/λα is a real-valued function in h∞(D). Here h∞(D) is the set of all bounded harmonic functions on the open unit disk D. [ABSTRACT FROM AUTHOR]