Factorization in $SL^\infty$

TL;DR

This paper proves that the non-separable Banach space $SL^$ is primary by directly solving its infinite dimensional factorization problem, avoiding Bourgain's localization method.

Contribution

It introduces a new direct approach to the factorization problem in $SL^$, establishing its primarity without relying on existing localization techniques.

Findings

$SL^$ is a primary Banach space.

Direct solution to the infinite dimensional factorization problem.

Bypasses Bourgain's localization method.

Abstract

We show that the non-separable Banach space $SL^\infty$ is primary. This is achieved by directly solving the infinite dimensional factorization problem in $SL^\infty$. In particular, we bypass Bourgain's localization method.