Rationalized Toeplitz Hankel operators via operator equations

Abstract

In this paper, we compute and study the behaviour of the solutions of the equation λ^k₂ M_z^k2 X = XM_z^k1 . Precisely, for a general complex number λ and non-zero integers k₁ and k₂, we introduce λ-Rationalized Toeplitz Hankel operators X on the space L²(λ − RT HO(L²)) as the solution of the equation λ^k₂ M_z^k2 X = XM_z^k1. We discuss some properties of solution of these operator equations.