The Hahn-Banach theorem in spaces of nonlinear generalized functions

2024/10/11 by Kebiche, Djamel eddine, Giordano, Paolo
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2410.08679

Abstract

In this paper, we establish a suitable version of the Hahn-Banach theorem within the framework of Colombeau spaces, a class of spaces used to model generalized functions. Our approach addresses the case where maps are defined ε-wise, which simplifies the framework and makes the extension of linear functionals more manageable. As an application of our main result, we demonstrate the separation of convex sets in Colombeau spaces.

Related

• Uniqueness of Hahn-Banach extensions in locally convex spaces
• A convenient notion of compact set for generalized functions
• Another proof of the analytic Hahn-Banach Theorem
• A new form of the Hahn-Banach Theorem
• Some problems in functional analysis inspired by Hahn Banach type theorems