English

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

Functional Analysis 2021-01-05 v1

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.

Keywords

Cite

@article{arxiv.2101.00653,
  title  = {Uniform Boundedness Principle and Hahn-Banach Theorem for b-linear functional related to linear 2-normed space},
  author = {Prasenjit Ghosh and Sanjay Roy and T. K. Samanta},
  journal= {arXiv preprint arXiv:2101.00653},
  year   = {2021}
}

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17 pages