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arXiv · 2101.04555

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

Prasenjit Ghosh·T. K. Samanta
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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.

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Prasenjit Ghosh, T. K. Samanta. 2021-01-12. Representation of Uniform Boundedness Principle and Hahn-Banach Theorem in linear n-normed space. https://doi.org/10.1007/s41478-021-00358-x

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