doi: 10.17706/ijapm.2016.6.1.25-30
Some Formulae of n-Norms and Their Identicalness in a Hilbert Space
- Manipur University, Canchipur, Imphal, Manipur, India
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.<br /> 2010 Mathematics Subject Classification: 46B20, 46C05, 46C15, 46B99, 46C99.
Keywords
- Dual space
- Hilbert space
- inner product
- norm
- n-norm
- separable space
How to Cite
M. P. Singh and 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. https://doi.org/ 10.17706/ijapm.2016.6.1.25-30
Copyright & License
Copyright © 2016 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).