1Kernels of bounded operators on the classical transfinite Banach sequence spaces

Arnott, Max and Laustsen, Niels Jakob (2025) 1Kernels of bounded operators on the classical transfinite Banach sequence spaces. In: Banach Algebras and Harmonic Analysis : Arens Products, Factorizations, and Bounded Operators. de Gruyter, pp. 1-12. ISBN 9783111643243

Abstract

Every closed subspace of each of the Banach spaces X = ℓ p ( Γ ) and X = c 0 ( Γ ) , where Γ is a set and 1 < p < ∞ , is the kernel of a bounded operator X → X . On the other hand, whenever Γ is an uncountable set, ℓ 1 ( Γ ) contains a closed subspace that is not the kernel of any bounded operator ℓ 1 ( Γ ) → ℓ 1 ( Γ ) .