On the essential spectrum of λ-Toeplitz operators over compact Abelian groups

In the recent paper by Mark C. Ho (2014) the notion of a λ-Toeplitz operator on the Hardy space H2(T) over the one-dimensional torus T was introduced and it was shown (under the supplementary condition) that for λ∈T the essential spectrum of such an operator is invariant with respect to the rotation z↦λz; if in addition λ is not of finite order the essential spectrum is circular. In this paper, we generalize these results to the case when T is replaced by an arbitrary compact Abelian group whose dual is totally ordered.