Approximate Representation of Bergman Submodules

作     者：Chong ZHAO 

作者机构：School of Mathematics Shandong University 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2016年第37卷第2期

页      面：221-234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 the National Natural Science Foundation of China(Nos.11271075,11371096) Shandong Province Natural Science Foundation(No.ZR2014AQ009) the Fundamental Research Funds of Shandong University(No.2015GN017) 

主　　题：Approximate representation Essential normality Bergman submodule 

摘      要：In the present paper, the author shows that if a homogeneous submodule M of the Bergman module L_a^2(B_d) satisfies P_M-sum from i to ( M_(zi)P_MM*_(zi))≤c/(N + 1)P_M for some number c 0, then there is a sequence {f_j } of multipliers and a positive number c such that c P_M ≤sum from j to ( M_(fj)M*_(fj))≤ P_M, i.e., M is approximately representable. The author also proves that approximately representable homogeneous submodules are p-essentially normal for p d.