A surjective summation operator with no Lipschitz right inverse

Laustsen, Niels Jakob; Messerschmidt, Miek; Wortel, Marten

doi:10.1090/proc/16496

A surjective summation operator with no Lipschitz right inverse
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by Niels Jakob Laustsen, Miek Messerschmidt and Marten Wortel;

Proc. Amer. Math. Soc. 152 (2024), 253-266

DOI: https://doi.org/10.1090/proc/16496

Published electronically: October 24, 2023

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Abstract:

We show that there exists a Banach space $X$ which contains closed subspaces $Y$ and $Z$ with $Y+Z=X$ such that the associated surjective summation operator $\Sigma \colon Y\times Z\to X$ defined by $\Sigma (y,z)= y+z$ for $y\in Y$ and $z\in Z$ has no Lipschitz right inverse.

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