Abstract—The aim of this paper is to investigate bounded linear functionals on an n-normed space with respect to norms of its quotient spaces. These norms will be our main tools as well as a new viewpoint. We will give several types of boundedness of bounded linear functionals on an n-normed space and investigate the dual spaces that corresponds to each type of boundedness. We obtain the relations between all types of boundedness, which correspond to the inclusion relations between the dual spaces.

Index Terms—Bounded linear functionals, n-normed spaces, quotient spaces.

The authors are with Analysis and Geometry Research Group, Bandung Institute of Technology, Bandung, West Java, Indonesia (email: h.batkunde@fmipa.unpatti.ac.id).

Cite: Harmanus Batkunde, Hendra Gunawan "Bounded Linear Functional on n-Normed Spaces through Its Quotient Spaces," International Journal of Applied Physics and Mathematics vol. 10, no. 2, pp. 81-87, 2020.

Copyright © 2020 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).