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arXiv · 2503.12940

Kernels of Bounded Operators on the Classical Transfinite Banach Sequence Spaces

Max Arnott·Niels Jakob Laustsen
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Abstract

Every closed subspace of each of the Banach spaces $X = \ell_p(\Gamma)$ and $X=c_0(\Gamma)$, where $\Gamma$ is a set and $1<p<\infty$, is the kernel of a bounded operator $X\to X$. On the other hand, whenever $\Gamma$ is an uncountable set, $\ell_1(\Gamma)$ contains a closed subspace that is not the kernel of any bounded operator $\ell_1(\Gamma)\to\ell_1(\Gamma)$.

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Max Arnott, Niels Jakob Laustsen. 2025-03-17. Kernels of Bounded Operators on the Classical Transfinite Banach Sequence Spaces. https://arxiv.org/abs/2503.12940

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