Banach空间的线性嵌入理论及算子分解  

Linear embedding and factorizations of operators on Banach spaces

作　　者：郑本拓 Bentuo Zheng

机构地区：[1]Department of Mathematical Sciences,University of Memphis,Memphis,TN 38152,USA

出　　处：《中国科学：数学》2020年第12期1923-1938,共16页Scientia Sinica：Mathematica

基　　金：Simons基金会(批准号:585081)资助项目。

摘　　要：线性嵌入理论是Banach空间几何学研究的核心领域之一,而算子分解理论是同胚理论的一个自然扩展和延伸.本文首先详细介绍关于线性同胚理论的主要结果,然后阐述该领域近期取得的一些重要进展,之后对算子分解的相关定理进行讨论,最后提出一些本领域尚未解决的遗留问题.Embedding theory is one of the most important topics in the geometry of Banach spaces and factorizations of operators are the natural extensions. In this paper, we will first systematically introduce the historical results on isomorphic theory and present some of the recent progress in this direction. Then we will discuss related results about factorizations of operators. Interesting open problems will be listed at the end of the paper.

关 键 词：线性嵌入 线性同胚 算子分解 SCHAUDER基 无条件基 

分 类 号：O177.2[理学—数学]