Representation of Uniform Boundedness Principle and Hahn-Banach Theorem in linear n-normed space

Abstract

The concept of b-linear functional and its different types of continuity in linear n-normed space are presented and some of their properties are being established. We derive the Uniform Boundedness Principle and Hahn-Banach extension Theorem with the help of bounded b-linear functionals in the case of linear n-normed spaces and discuss some examples and applications. Finally, we present the concept of weak*convergence for the sequence of bounded b-linear functionals in linear n-normed space.

arXiv comment22 pages. arXiv admin note: text overlap with arXiv:2101.00653