A Schwarz Lemma at the Boundary of Hilbert Balls

作     者：Zhihua CHEN Yang LIU Yifei PAN 

作者机构：Department of Mathematics Tongji UniversityShanghai 200092 China. Corresponding author. Department of Mathematics Zhejiang Normal University Jinhua 321004Zhejiang China. Department of Mathematical Sciences Indiana University-Purdue University Fort Wayne Fort Wayne IN 46805-1499 USA School of Mathematics and Informatics Jiangxi Normal University Nanchang 330022 China. 

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

年 卷 期：2018年第39卷第4期

页      面：695-704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.11671361,11571256) the Zhejiang Provincial Natural Science Foundation of China(No.LY14A010008) 

主　　题：Boundary Schwarz lemma Separable Hilbert space Holomorphic mapping Unit ball 

摘      要：In this paper, the authors prove a general Schwarz lemma at the boundary for the holomorphic mapping f between unit balls B and B＇ in separable complex Hilbert spaces H and H＇, respectively. It is found that if the mapping f ∈ C^1＋α at z0 ∈ B with f（zo） = wo ∈ OB＇, then the Fr＆het derivative operator Df（z0） maps the tangent space Tz0（ B^n） to Tw0（ B＇）, the holomorphic tangent space Tz0^（1,0） to Tw0（1,0）（ B＇）,respectively.