DOI: 10.24193/fpt-ro.2025.2.17

Authors: J.R. Acosta-Portilla and L.Y. Garrido-Ramirez

Abstract: Let (X, ‖ · ‖) be a Banach space and C a nonempty subset of X. We will say that a norm for the Banach space of bounded Lipschitzian mappings BLip(C, X) is ‖ · ‖-constructible if that depend only on the infinity norm ‖ · ‖_∞ and the Lipschitz constant K( · , ‖ · ‖ ). In this work we characterize the ‖ · ‖-constructible norms such as those that does not separate ‖ · ‖-indistinguishable operators, and we characterize constructible norms ‖ · ‖₀ like those which are φ(‖ · ‖₀)-constructible where φ(‖ · ‖₀) is the projection of ‖ · ‖₀ over the space X.

Key Words and Phrases: Lipschitzian mappings, renorming of Banach spaces, constructible norm.

2010 Mathematics Subject Classification: 26B99, 46B03, 46B20, 47H09, 47H10.

Published on-line: May 1st, 2025.

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