Identicalness of n-norms

Abstract

In this paper, we discuss the concept of n-norm and n-normed spaces. Further we prove the equality of seven formulae of n-norms on a Hilbert space and eight formulae of n-norms on a separable Hilbert space. An alternative formula of n-norm on the dual of an n-normed space is introduced. Also, we show its equality with two alternative formulae.