Abstract—In this paper, we discuss the concept of n-normed spaces and generalize a formulae of n-norm. 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.
2010 Mathematics Subject Classification: 46B20, 46C05, 46C15, 46B99, 46C99.

Index Terms—Dual space, Hilbert space, inner product, norm, n-norm, separable space.

The authors are with Manipur University, Canchipur, Imphal, Manipur, India (email: mpremjitmu@gmail.com).

Cite: M. P. Singh, S. Romen Meitei, "Some Formulae of n-Norms and Their Identicalness in a Hilbert Space," International Journal of Applied Physics and Mathematics vol. 6, no. 1, pp. 25-30, 2016.