Analytic Toeplitz algebras and the Hilbert transform associated with a subdiagonal algebra

作     者：JI GuoXing 

作者机构：College of Mathematics and Information Science Shaanxi Normal University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2014年第57卷第3期

页      面：579-588页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant No.11371233) the Fundamental Research Funds for the Central Universities(Grant No.GK201301007) 

主　　题：von Neumann algebra subdiagonal algebra noncommutative Hp space Toeplitz operator Hilbert transform 

摘      要：Let M be a a-finite yon Neumann algebra and let 9i C M be a maximal subdiagonal algebra with respect to a faithful normal conditional expectation Ф. Based on the Haagerup＇s noncommutative Lp space LP（M） associated with M, we consider Toeplitz operators and the Hilbert transform associated with 8i. We prove that the commutant of left analytic Toeplitz algebra on noncommutative Hardy space H2（A4） is just the right analytic Toeplitz algebra. Furthermore, the Hilbert transform on noncommutative LP（Yt4） is shown to be bounded for 1 （ p （ ce. As an application, we consider a noncomnmtative analog of the space BMO and identify the dual space of noncommutative Hl（M） as a concrete space of operators.