The conditions that the Toeplitz operator is normal or analytic (Q1812278)

The first examples of subnormal Toeplitz operators on the Hardy space \(H^2\) that are neither normal nor analytic were found by \textit{C. C. Cowen} and \textit{J. J. Long jun.} [J. Reine Angew. Math. 351, 216--220 (1984; Zbl 0532.47019)], thus answering a question posed by P. Halmos in 1970. The purpose of the present paper is to give new sufficient conditions under which a Toeplitz operator is normal or analytic; these conditions extend previous results due to \textit{M. B. Abrahamse} [Duke Math. J. 43, 597--604 (1976; Zbl 0332.47017)].