关于复Banach空间的几何学  

On Geometry of Complex Banach Spaces

作　　者：刘培德[1] 侯友良[1] 

机构地区：[1]武汉大学数学系

出　　处：《数学进展》1998年第1期1-20,共20页Advances in Mathematics（China）

基　　金：国家自然科学基金

摘　　要：本文介绍复Ｂａｎａｃｈ空间几何学近年来的发展状况及其与向量值调和分析、Ｂ值鞅理论的联系．文章包括以下内容：１．几个反例；２．复凸性与复凸模；３．解析Ｒａｄｏｎ－Ｎｉｋｏｄｙｍ性质的分析特征；４．解析Ｒａｄｏｎ－Ｎｉｋｏｄｙｍ性质的几何特征；５．几种ＲＮ性质的比较；６．ＰＬ一致凸性的鞅刻画；７．Ｈ一致凸性的鞅刻画；８．向量值Ｈａｒｄｙ与Ｐａｌｅｙ不等式；９．解析ＵＭＤ空间．In this paper, recent devolopments of geometry of complex Banach spaces and relationships between them and vector-valued harmonic analysis, martingale theory have been introduced. It carries on in the following nine aspects: 1. Some counterexamples; 2. Complex convexity and moduli of complex convexity; 3. Analytic charactorizations of ARNP; 4. Geometric charactorizations of ARNP; 5. Comparation between several RNP’s; 6. Martingale charactorizations for PL uniform convexity; 7. Martingale characterizations for H uniform convexity; 8. Vector valued Hardy and Paley inequalities; 9. AUMD spaces.

关 键 词：复空间几何学 复巴拿赫空间 几何学 

分 类 号：O177.2[理学—数学]