Kernels of bounded operators on the classical transfinite Banach sequence spaces

Arnott, Max and Laustsen, Niels (2025) Kernels of bounded operators on the classical transfinite Banach sequence spaces. In: Banach algebras and harmonic analysis :. de Gruyter. (In Press)

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Abstract

Every closed subspace of each of the Banach spaces X=lp(Γ) and X=c0(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, l1(Γ) contains a closed subspace that is not the kernel of any bounded operator l1(Γ)→l1(Γ).