Functions and Analysis


An Extension Theorem of Nonlinear Lipschitz Functional and its Application in Banach Spaces

Authors: Choe Ryong Gil

In this paper we have obtained a new theorem that a nonlinear Lipschitz (Lip-) functional defined on the closed subset of Banach spaces can be extended to the whole space with Lip-continuity and maintenance of Lip-constant, which would be called an extension theorem (ET). This theorem is a generalization to the Lip-functional of the famous Hahn-Banach theorem on the bounded linear functional. By the ET, we have completely solved the open problem on the relation of the invertibility between the Lip-operator and its Lip-dual operator.

Comments: 17 pages

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Submission history

[v1] 2012-02-19 02:03:52

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