Serre&apos;s Renorming Problem

Albert Kubzdela

doi:10.36045/j.bbms.231108

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Title

Serre's Renorming Problem

Authors

Albert Kubzdela (WILiT) ^{[ 1 ][ 7.4 ][ P ]}

^{[ 1 ]} Instytut Inżynierii Lądowej, Wydział Inżynierii Lądowej i Transportu, Politechnika Poznańska | ^{[ P ]} employee

Scientific discipline (Law 2.0)

[7.4] Mathematics

Year of publication

2024

Published in

Bulletin of the Belgian Mathematical Society - Simon Stevin

Journal year: 2024 | Journal volume: vol. 31 | Journal number: no. 1

Article type

scientific article

Publication language

english

Keywords

EN

Non-Archimedean normed spaces
Renorming problem

Abstract

EN Let K be a non-archimedean complete valued field and let (E,∥.∥) be a non-archimedean normed space over K. Let |K×|:={|λ|:λ∈K∖{0}} and ∥E×∥:={∥x∥:x∈E∖{0}}. By Serre's Renorming Problem we mean the following question: can one for every non-archimedean normed space E introduce a norm ∥.∥∙ on E that is equivalent to the given norm in the sense that it determines the same topology and has the property ∥E×∥∙=|K×|? An affirmative solution of this problem is presented.

Pages (from - to)

102 - 114

DOI

10.36045/j.bbms.231108

URL

https://projecteuclid.org/journals/bulletin-of-the-belgian-mathematical-society-simon-stevin/volume-31/issue-1/Serres-Renorming-Problem/10.36045/j.bbms.231108.short

Ministry points / journal

70

Impact Factor

0,6 [List 2022]

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