On Toeplitz-Like Operators in L2h

Abstract

Let D = {z ∈ C : |z| < 1} be the open unit disc in the complex plane C. Let L²_h(ID) be the subspace of functions in L²(D) that are harmonic. Let Q be the orthogonal projection of L² onto L²_h. For Φ ∈ L^∞;(D), define L_Φ from L²_h into itself such that LΦf= Q(Φf). In this paper some algebraic properties of the Toeplitz-like operator L_Φ are derived.