Geodesic
The $n$-dual space of the space of $p$-summable sequences
Mathematica Bohemica, Tome 138 (2013) no. 4, pp. 439-448

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In the theory of normed spaces, we have the concept of bounded linear functionals and dual spaces. Now, given an $n$-normed space, we are interested in bounded multilinear $n$-functionals and $n$-dual spaces. The concept of bounded multilinear $n$-functionals on an $n$-normed space was initially intoduced by White (1969), and studied further by Batkunde et al., and Gozali et al. (2010). In this paper, we revisit the definition of bounded multilinear $n$-functionals, introduce the concept of $n$-dual spaces, and then determine the $n$-dual spaces of $\ell^p$ spaces, when these spaces are not only equipped with the usual norm but also with some $n$-norms.
In the theory of normed spaces, we have the concept of bounded linear functionals and dual spaces. Now, given an $n$-normed space, we are interested in bounded multilinear $n$-functionals and $n$-dual spaces. The concept of bounded multilinear $n$-functionals on an $n$-normed space was initially intoduced by White (1969), and studied further by Batkunde et al., and Gozali et al. (2010). In this paper, we revisit the definition of bounded multilinear $n$-functionals, introduce the concept of $n$-dual spaces, and then determine the $n$-dual spaces of $\ell^p$ spaces, when these spaces are not only equipped with the usual norm but also with some $n$-norms.
DOI : 10.21136/MB.2013.143516
Classification : 46B20, 46B99, 46C05, 46C15, 46C99
Keywords: $\ell^p$ space; $n$-normed space; $n$-dual space 
Pangalela, Yosafat E. P.; Gunawan, Hendra. The $n$-dual space of the space of $p$-summable sequences. Mathematica Bohemica, Tome 138 (2013) no. 4, pp. 439-448. doi: 10.21136/MB.2013.143516
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