Factorization in $S{L}^{\infty }$

Abstract

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

17 pages, 1 figure

References in corpus (3)

• Factorization of the identity through operators with large diagonal
• Factorization in mixed norm Hardy and BMO spaces
• Localization and projections on bi-parameter BMO

Cited by in corpus (3)

• Factorization of the identity through operators with large diagonal
• Dimension dependence of factorization problems: Hardy spaces and $S{L}_n^{\infty }$
• Continuous factorization of the identity matrix