DUAL SPACE OF THE SPACE OF BOUNDED LINEAR n−FUNCTIONALS

Abstract

In [2] are considered \(n\)-Banach spaces, and in [4] are considered bounded and continuous linear \(n\)-functionals defined on \(n\)-normed space and several theorems connected with them, are proved. Then is proved that: Linear \(n\)-functional \(F\) is continuous if and only if \(F\) is bounded (theorem 4). In this paper, a dual space \(X^*\) of space of bounded linear \(n\)-functionals is considered and it is proved that: if \(X\) is \(n\)-Banach space than \((X^*, \lVert \cdot \rVert)\) is Banach space.