Abstract
Recently, Alonso showed that every two-dimensional normed space is isometrically isomorphic to a generalized Day-James space introduced by Nilsrakoo and Saejung. In this paper, we consider the result of Alonso for n-dimensional normed spaces.MSC:46B20.
Highlights
Alonso showed that every two-dimensional normed space is isometrically isomorphic to a generalized Day-James space introduced by Nilsrakoo and Saejung
In, Nilsrakoo and Saejung [ ] introduced and studied generalized Day-James spaces φ - ψ, where φ - ψ is defined for φ, ψ ∈ as the space R endowed with the Tanaka and Saito Journal of Inequalities and Applications 2012, 2012:284 http://www.journalofinequalitiesandapplications.com/content/2012/1/284 norm
Alonso [ ] showed that every two-dimensional normed space is isometrically isomorphic to a generalized Day-James space
Summary
A norm · on R is said to be absolute if (x, y) = (|x|, |y|) for all (x, y) ∈ R , and normalized if ( , ) = ( , ) = . The set of all absolute normalized norms on R is denoted by AN . The Day-James space p- q is defined for ≤ p, q ≤ ∞ as the space R endowed with the norm
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