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.

Item Type:
Journal Article
Journal or Publication Title:
Proceedings of the American Mathematical Society
Uncontrolled Keywords:
Research Output Funding/yes_externally_funded
Subjects:
?? banach spacesummation operatorsurjectionright inverselipschitz mapyes - externally fundedmathematics(all)applied mathematics ??
ID Code:
190435
Deposited By:
Deposited On:
13 Apr 2023 13:15
Refereed?:
Yes
Published?:
In Press
Last Modified:
28 Jun 2024 02:19