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

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