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 and Phrases
Linear 2-normed space, 2-Banach space, Closed operator, Uniform Boundedness Principle, Hahn-Banach extension Theorem.
A.M.S. subject classiﬁcation
46A22, 46B07, 46B25.