Extendibility of bilinear forms on Banach sequence spaces

TL;DR

This paper investigates the conditions under which bilinear forms on Banach sequence spaces can be extended to larger spaces, providing characterizations and identifying spaces with universal extension properties.

Contribution

It characterizes $c_0$ via bilinear form extension properties and describes Banach sequence spaces allowing universal bilinear form extensions.

Findings

Characterization of $c_0$ through bilinear form extension properties

Identification of Banach sequence spaces with universal extension capabilities

Conditions for extending bilinear forms to superspaces

Abstract

We study Hahn-Banach extensions of multilinear forms defined on Banach sequence spaces. We characterize $c_0$ in terms of extension of bilinear forms, and describe the Banach sequence spaces in which every bilinear form admits extensions to any superspace.