Equivalence relations of n-norms on a vector space

Authors

  • Tyas Rangga Kristiantoo Department of Mathematics, Bandung Institute of Technology, Bandung, Indonesia Author
  • Raden Akbar Wibawa-Kusumah Department of Mathematics, Bandung Institute of Technology, Bandung, Indonesia Author
  • Hendra Gunawan Department of Mathematics, Institut Teknologi Bandung, Bandung, Indonesia Author

Keywords:

n-normed spaces, equivalence relations

Subjects:

46B05, 46B20, 46A99, 46B99

Abstract

A vector space can be equipped with more than one n-norm. In such a case, an equivalencerelation of n-norms is usually studied. Here we discuss andpresent some results on several equivalence relations of n-normswhich may be defined on a vector space. In particular, our resultscorrect an error that we found in B.S. Reddy, H. Dutta, [Onequivalence of n-norms in n-normed spaces, preprint, {http://www.akamaiuniversity.us/PJST11\_1\_233.pdf}, March 7,2011]. We also discuss an equivalence relation of n-norms on finite dimensional spaces.

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Published

2013-10-15