Bi-dual and Reflexivity of Cone Normed Space

Authors

  • Anas Yusuf Federal University, Birnin Kebbi, Kebbi State, Nigeria
  • Musa Kallamu Federal University, Birnin Kebbi, Kebbi State, Nigeria

DOI:

https://doi.org/10.57233/ijsgs.v10i1.587

Keywords:

Dual, Bi-dual, Reflexivity, Cone normed space, Weak* topology

Abstract

A cone normed space is one of the generalizations of normed space in which the codomain of normed space is replaced by an ordered real Banach space. In this paper, some properties of the dual, in particular bi-dual in the setting of cone normed space were studied. This allows us to define the notion of reflexivity with respect to cone normed space and proved the necessary and sufficient condition for a cone normed space to be reflexive.

Author Biographies

Anas Yusuf, Federal University, Birnin Kebbi, Kebbi State, Nigeria

Department of Mathematics, Federal University, Birnin Kebbi, Kebbi State, Nigeria

Musa Kallamu, Federal University, Birnin Kebbi, Kebbi State, Nigeria

Department of Mathematics, Federal University, Birnin Kebbi, Kebbi State, Nigeria

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Published

2024-03-31

How to Cite

Yusuf, A. ., & Kallamu, M. . (2024). Bi-dual and Reflexivity of Cone Normed Space. International Journal of Science for Global Sustainability, 10(1), 24–28. https://doi.org/10.57233/ijsgs.v10i1.587

Issue

Vol. 10 No. 1 (2024): INTERNATIONAL JOURNAL OF SCIENCE FOR GLOBAL SUSTAINABILITY

Section

Articles

License

Copyright (c) 2024 Author(s)

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This work is licensed under a Creative Commons Attribution 4.0 International License.