$n$-dual spaces associated to a normed space

Abstract

For a real normed space $X$, we study the $n$-dual space of $\left(X,\Vert \cdot \Vert \right)$ and show that the space is a Banach space. Meanwhile, for a real normed space $X$ of dimension $d\ge n$ which satisfies property (G), we discuss the $n$-dual space of $\left(X,{\Vert \cdot ,\dots ,\cdot \Vert }_G\right)$, where is the Gähler $n$% -norm. We then investigate the relationship between the $n$-dual space of and the $n$-dual space of . We use this relationship to determine the $n$-dual space of $\left(X,{\Vert \cdot ,\dots ,\cdot \Vert }_G\right)$and show that the space is also a Banach space.

arXiv commentTo appear in Khayyam Journal of Mathematics

Cited by in corpus (1)

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