Serre's Renorming Problem
[ 1 ] Instytut Inżynierii Lądowej, Wydział Inżynierii Lądowej i Transportu, Politechnika Poznańska | [ P ] pracownik
2024
artykuł naukowy
angielski
- Non-Archimedean normed spaces
- Renorming problem
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.
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