The $n$-dual space of the space of $p$-summable sequences

Pangalela, Yosafat E. P., and Gunawan, Hendra. "The $n$-dual space of the space of $p$-summable sequences." Mathematica Bohemica 138.4 (2013): 439-448. <http://eudml.org/doc/260741>.

@article{Pangalela2013,
abstract = {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.},
author = {Pangalela, Yosafat E. P., Gunawan, Hendra},
journal = {Mathematica Bohemica},
keywords = {$\ell ^p$ space; $n$-normed space; $n$-dual space; space; -normed space; -dual space},
language = {eng},
number = {4},
pages = {439-448},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The $n$-dual space of the space of $p$-summable sequences},
url = {http://eudml.org/doc/260741},
volume = {138},
year = {2013},
}

TY - JOUR
AU - Pangalela, Yosafat E. P.
AU - Gunawan, Hendra
TI - The $n$-dual space of the space of $p$-summable sequences
JO - Mathematica Bohemica
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 138
IS - 4
SP - 439
EP - 448
AB - 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.
LA - eng
KW - $\ell ^p$ space; $n$-normed space; $n$-dual space; space; -normed space; -dual space
UR - http://eudml.org/doc/260741
ER -