The Commutant of Analytic Toeplitz Operators on Bergman Space  

作　　者：Yu Cheng LI 

机构地区：[1]Department of Mathematics, Hebei Normal University, Shijiazhuang 050016, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2008年第10期1737-1750,共14页数学学报（英文版）

基　　金：the National Natural Science Foundation of China(10571041);the Doctoral Foundation of Hebei Normal University(130144)

摘　　要：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^ng（z） （n ≥1）, g（z） = b0 ＋ b1z^p1 ＋b2z^p2 ＋.. , bk ≠ 0 （k = 0, 1, 2,...）, our main result is =A′（Mf） = A′（Mzn）∩A′（Mg） = A′（Mz^s）, 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.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^ng（z） （n ≥1）, g（z） = b0 ＋ b1z^p1 ＋b2z^p2 ＋.. , bk ≠ 0 （k = 0, 1, 2,...）, our main result is =A′（Mf） = A′（Mzn）∩A′（Mg） = A′（Mz^s）, 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.

关 键 词：Bergman space analytic Toeplitz operator COMMUTANT strong irreducibility 

分 类 号：O17[理学—数学]