The commutant of analytic toeplitz operators

作     者：Deddens, James A. Wong, Tin Kin 

作者机构：Department Of Mathematics University Of Kansas United States Department Of Mathematics Wayne State University United States 

出 版 物：《Transactions of the American Mathematical Society》 (Trans. Am. Math. Soc.)

年 卷 期：1973年第184卷

页      面：261-273页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Analytic function inner and outer functions ">  "> analytic Toeplitz operator pure is ometry commutant 

摘      要：In this paper we study the commutant of an analytic Toeplitz operator* For cf e H°°9 let cp — xF be its inner-outer factorization* Our main result is that if there exists X € C such that X factors as X = xi*2each X an inner function, and if F — X is divisible by each X,-, then \T$j =s j n\TpjThe key step in the proof is Lemma 2, which is a curious result about nilpotent operators* One corollary of our main result is that if X(z)= zn, n ^ 1, then\T1# p\\another is that if € H°° isunivalent then \T* =\TZ\ • We are also able to prove that if the inner factor of 4 is X(z) = zn, n £ 1, then \T p\1 = {TzS\1 where s is a positive integer maximal with respect to the property that zn and F(z) are both functions of zs» We conclude by raising six uestions. © 1973 American Mathematical Society.