非线性Lipschitz算子半群的表示

本文通过引入若干Lipschitz对偶概念,将非线性Lipschitz算子半群对偶映射到Lipschitz对偶空间中,使其转化为线性算子半群。该线性算子半群被证明是一个C_0~*-半群,因而是某个C_0-半群的对偶半群。从而证明了,在等距意义下,一个非线性Lipschitz算子半群可以延拓为一个C_0-半群。基于这些结论,本文给出了一系列全新的非线性Lipschitz算子半群的表示公式。

Representation Formulas for Nonlinear Semigroups of Lipschitz Operators

This paper is concerned with the representation problem of nonlinear semi- group of Lipschitz operators. By developing a series of novel dual notions of Banach space and Lipschitz operator, it is shown that a nonlinear semigroup of Lipschitz op- erators can induce a C_0~*-semigroup in Lipschitz dual space. Hence, it is proved that a nonlinear semigroup of Lipschitz operators can be isometrically embedded into a certain C_0-semigroup. On the basis of these results, a series of novel representation formulas for this type of nonlinear semigroup are therefore established.