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Владикавказский математический журнал, 2004, том 6, номер 1, страницы 26–28
(Mi vmj192)
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Non-uniqueness of certain Hahn–Banach extensions
E. Beckenstein, L. Narici Mathematics Department, St. John's University, Staten Island, NY, USA
Аннотация:
Let $f$ be a continuous linear functional defined on a subspace $M$ of a normed space $X$. If $X$ is real or complex, there are results that characterize uniqueness of continuous extensions $F$ of $f$ to $X$ for every subspace $M$ and those that apply just to $M$. If $X$ is defined over a non-Archimedean valued field $K$ and the norm also satisfies the strong triangle inequality, the Hahn–Banach theorem holds for all subspaces $M$ of $X$ if and only if $K$ is spherically complete and it is well-known that Hahn–Banach extensions are never unique in this context. We give a different proof of non-uniqueness here that is interesting for its own sake and may point a direction in which further investigation would be fruitful.
Поступила в редакцию: 24.03.2004
Образец цитирования:
E. Beckenstein, L. Narici, “Non-uniqueness of certain Hahn–Banach extensions”, Владикавк. матем. журн., 6:1 (2004), 26–28
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/vmj192 https://www.mathnet.ru/rus/vmj/v6/i1/p26
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