On T-u-Toeplitzness of weighted composition operators on H-2

Abstract

In this paper, we show that W-f,W-phi is T-u-Toeplitz if and only if C(phi)u = u, where u is a nonconstant inner function. We also provide necessary and sufficient conditions for T-u-Toeplitzness of W-f,W-phi* W-f,W-phi. Indeed, W-f,W-phi* W-f,W-phi is T-u-Toeplitz if and only if phi is an inner function. Finally, we study several conditions for the product Wf,phi Wf,phi* to be Toeplitz.