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Completeness of constructible norms
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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BibTeX
@misc{acostaportilla2026completeness,
title = {{Completeness of constructible norms}},
author = {Juan Rafael Acosta-Portilla and Armando Sánchez-Nungaray and Gerardo Ramos-Vázquez and Lizbeth Yolanda Garrido-Ramírez},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11782},
eprint = {2609.11782},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11782},
}
RIS
TY - UNPB
TI - Completeness of constructible norms
AU - Juan Rafael Acosta-Portilla
AU - Armando Sánchez-Nungaray
AU - Gerardo Ramos-Vázquez
AU - Lizbeth Yolanda Garrido-Ramírez
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11782
UR - https://arxiv.org/abs/2609.11782
AB - 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.
ER -