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Banach空间的Lipschitz对偶及其应用 被引量:6

A Novel Dual Notion of a Banach Space: Lipschitz Dual Space
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摘要 本文引进Banach空间E的一个全新对偶空间概念—Lipschitz对偶空间,并证明:任何Banach空间的Lipschitz对偶空间是某个包含E的Banach空间的线性对偶空间,以所引进的新对偶空间为框架,本文定义了非线性Lipschitz算子的Lipshitz对偶算子,证明:任何非线性Lipschitz算子的Lipschitz对偶算子是有界线性算子.所获结果为推广线性算子理论到非线性情形(特别,运用线性算子理论研究非线性算子的特性)开辟了一条新的途径.作为例证,我们应用所建立的理论证明了若干新的非线性一致Lipschitz映象遍历收敛性定理. A new dual space notion of a Banach space, named Lipschitz dual space,is introduced, and within the new introduced space framework, the concept of the Lipschitz dual operator of a nonlinear Lipschitz operator is further defined. It is proved that the Lipschitz dual space of any Banach space E is an ordinary dual space of a certain Banach space containing E in the isometric embeding sense, and that the Lipschitz dual operator of any nonlinear Lipscitz operator becomes linear and bounded.By means of these findings, a lot of important results in linear analysis and theorems on linear operators are generalized to nonlinear cases. Thereby, a completely new way to generalize the linear operator theory to the nonlinear case is developed. As examples,several new mean ergodic theorems of the uniformly Lipschitz operators are proved.
出处 《数学学报(中文版)》 SCIE CSCD 北大核心 1999年第1期61-70,共10页 Acta Mathematica Sinica:Chinese Series
基金 西安交通大学科学研究基金 西安交通大学博士学位论文基金
关键词 对偶空间 巴拿赫空间 李普希兹对偶 非线性算子 Nonlinear Lipschitz operator, Lipschitz dual space, Lipschitz dual operator,Uniformly Lipschitz mapping, Mean ergodicity
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