Spectral Properties of Two Classes of Toeplitz Operators on H^p, 1 p ∞

In this study, we consider two classes of Toeplitz operators on H p, 1 p ∞: Toeplitz operators with unimodular symbols and Toeplitz operators whose spectra satisfy a specific geometric condition (the circular convexity condition).We give some inclusions for their spectrum and some estimates for their resolvents. Using obtained results, we show the existence of nontrivial invariant subspaces of these types of Toeplitz operators. This result gives a partially answer to the question of which type operators on a Banach space has a nontrivial invariant subspace.