A remark on the essential spectra of Toeplitz operators with bounded measurable coefficients (Q877858)

Let \(\mathbb T\) be the unit circle and consider the Hardy space \(H^p(\mathbb T):=P L^p(\mathbb T)\), where \(P\) is the Riesz projection and \(1<p<\infty\). The paper presents a sufficient condition for a point to belong to the essential spectrum of a Toeplitz operator \(T(a) : H^p(\mathbb T) \to H^p(\mathbb T)\), \(T(a)f = P(af)\), generated by a function \(a\in L^\infty(\mathbb T)\). The condition is based on geometric properties of the cluster values of \(a\).