On the spectrum of complex symmetric Toeplitz operators

Abstract

In this paper we focus on the spectrum of Toeplitz operators Tφ on the Hardy space H 2 of the unit disk D when φ is not continuous and especially when Tφ is a complex symmetric operator. Moreover, we show a necessary condition for Tφ to be complex symmetric, for φ belongs to subalgebra H∞ +C (T) of L∞ and we present a case of the continuity of the spectral function restricted to the space of Toeplitz operators.