\(l^\infty\) AS \(n\)-NORMED SPACE

Abstract

The concept of a \(n\)-norm on the vector space with dimension greater than \(n\), \(n>1\), was introduced by A. Misiak ([4]). It is multidimensional analogy of the concept of a norm. In [1], [2], [3] and [4] was proved several properties of the \(n\)-normed spaces. In this work we will prove that the space of the bounded real sequences with usual operations adding and product with scalar is a real \(n\)-normed space.