IJAPM 2016 Vol.6(1): 25-30 ISSN: 2010-362X
doi: 10.17706/ijapm.2016.6.1.25-30
doi: 10.17706/ijapm.2016.6.1.25-30
Some Formulae of n-Norms and Their Identicalness in a Hilbert Space
M. P. Singh, S. Romen Meitei
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).
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.
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ISSN: 2010-362X (Online)
Abbreviated Title: Int. J. Appl. Phys. Math.
Frequency: Quarterly
APC: 500USD
DOI: 10.17706/IJAPM
Editor-in-Chief: Prof. Haydar Akca
Abstracting/ Indexing: INSPEC(IET), CNKI, Google Scholar, EBSCO, Chemical Abstracts Services (CAS), etc.
E-mail: ijapm@iap.org
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