Extension of Operators from Weak$^*$-closed Subspaces of $\ell_1$

TL;DR

This paper proves that operators defined on weak$^*$-closed subspaces of ll_1 can be extended to the whole space, facilitating broader applications in functional analysis.

Contribution

It establishes a general extension theorem for operators from weak$^*$-closed subspaces of ll_1 to spaces of continuous functions.

Findings

Operators from weak$^*$-closed subspaces of ll_1 extend to ll_1

Extension preserves operator properties

Facilitates analysis of operators on ll_1

Abstract

It is proved that every operator from a weak$^*$-closed subspace of $\ell_1$ into a space $C(K)$ of continuous functions on a compact Hausdorff space $K$ can be extended to an operator from $\ell_1$ to $C(K)$.