A surjective summation operator with no Lipschitz right inverse

Laustsen, Niels and Messerschmidt, Miek and Wortel, Marten (2023) A surjective summation operator with no Lipschitz right inverse. Proceedings of the American Mathematical Society. ISSN 0002-9939 (In Press)

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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 Σ: Y×Z→X defined by Σ(y,z)= y+z for y∈Y and z∈Z has no Lipschitz right inverse.