For a real normed space $X$, we study the $n$-dual space of $\left( X,\left\Vert \cdot \right\Vert \right) $ and show that the space is a Banach space. Meanwhile, for a real normed space $X$ of dimension $d\geq n$ which satisfies property ($G$), we discuss the $n$-dual space of $\left( X,\left\Vert \cdot,\ldots ,\cdot \right\Vert _{G}\right) $, where $% \left\Vert \cdot ,\ldots ,\cdot \right\Vert _{G}$ is the Gähler $n$-norm. We then investigate the relationship between the $n$-dual space of $% \left( X,\left\Vert \cdot \right\Vert \right) $ and the $n$-dual space of $% \left( X,\left\Vert \cdot,\ldots ,\cdot \right\Vert _{G}\right) $. We use this relationship to determine the $n$-dual space of $\left( X,\left\Vert \cdot ,\ldots ,\cdot \right\Vert _{G}\right) ~$and show that the space is also a Banach space.
Pangalela, Y. E. (2015). $n$-Dual Spaces Associated to a Normed Space. Khayyam Journal of Mathematics, 1(2), 219-229. doi: 10.22034/kjm.2015.13166
MLA
Yosafat E.P. Pangalela. "$n$-Dual Spaces Associated to a Normed Space". Khayyam Journal of Mathematics, 1, 2, 2015, 219-229. doi: 10.22034/kjm.2015.13166
HARVARD
Pangalela, Y. E. (2015). '$n$-Dual Spaces Associated to a Normed Space', Khayyam Journal of Mathematics, 1(2), pp. 219-229. doi: 10.22034/kjm.2015.13166
VANCOUVER
Pangalela, Y. E. $n$-Dual Spaces Associated to a Normed Space. Khayyam Journal of Mathematics, 2015; 1(2): 219-229. doi: 10.22034/kjm.2015.13166
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