Nonatomic submeasures on $\mathbb{N}$ and the Banach space ${\ell }_1$

Abstract

Nonatomic bounded sequences in ${\ell }_1$, that is, those giving rise to nonatomic submeasures on $\mathbb{N}$ are introduced and shown to form a closed subspace nonat$({\ell }_1)$ of ${\ell }_{\infty }({\ell }_1)$, and some spaces of relevant operators in ${\ell }_1$ are considered.

arXiv comment6 pages