Equivalence relations of $n$-norms on a vector space
Keywords:
$n$-normed spaces, equivalence relationsSubjects:
46B05, 46B20, 46A99, 46B99Abstract
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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2013-10-15
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