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arXiv · 2101.00653

Uniform Boundedness Principle and Hahn-Banach Theorem for b-linear functional related to linear 2-normed space

Prasenjit Ghosh·Sanjay Roy·T. K. Samanta
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Abstract

In this paper, we will see that the Cartesian product of two 2-Banach spaces is also 2-Banach space and discuss some properties of closed linear operator in linear 2-normed space. We also describe the concept of different types of continuity of b-linear functional and derive the Uniform Boundedness Principle and Hahn-Banach extension theorem for b-linear functionals in the case of linear 2-normed spaces. We also introduce the notion of weak*convergence for the sequence of bounded b-linear functionals relative to linear 2-normed space.

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Prasenjit Ghosh, Sanjay Roy, T. K. Samanta. 2021-01-03. Uniform Boundedness Principle and Hahn-Banach Theorem for b-linear functional related to linear 2-normed space. https://arxiv.org/abs/2101.00653

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