The commutant of analytic Toeplitz operators on Bergman space

In this paper, using the matrix skills and operator theory techniques we characterize the commutant of analytic Toeplitz operators on Bergman space. For f(z) = z ⁿ g(z)(n ≥ 1), g(z) = b ₀ + b ₁ +b ₂ +···, b _k ≠ 0(k = 0, 1, 2, ...), our main result is (M _f ) = ()∩ (M _g ) = (), where s = g.c.d.(n,p1,p2,...). In the last section, we study the relation between strongly irreducible curve and the winding number W(f,f(α)), α ∈ D. This work is supported by the National Natural Science Foundation of China(10571041) and the Doctoral Foundation of Hebei Normal University(130144)