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arXiv · 2609.11782

Completeness of constructible norms

Juan Rafael Acosta-Portilla·Armando Sánchez-Nungaray·Gerardo Ramos-Vázquez·Lizbeth Yolanda Garrido-Ramírez
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Abstract

In the present work we study for a given Banach space the quotient of the family of equivalent norms modulus the collinearity relationship and prove that under a Banach-Mazur type metric this family is a complete metric space, and we also prove the completeness of the family of constructible norms for the Banach space of bounded Lipschitzian mappings between convex sets of a Banach space.

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Juan Rafael Acosta-Portilla, Armando Sánchez-Nungaray, Gerardo Ramos-Vázquez, Lizbeth Yolanda Garrido-Ramírez. 2026-09-10. Completeness of constructible norms. https://arxiv.org/abs/2609.11782

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