Hiroshima Mathematical Journal

On generalized $\bf{\ell_p}$-spaces

Ken-ichi Mitani and Kichi-Suke Saito

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Abstract

In our article Absolute norms on $C^n$,, we characterized absolute normalized norms on $\Bbb C^n$ by using a continuous convex function with some appropriate conditions on a certain convex subset of $\mathbb R^n$. In this paper, we introduce the notion of generalized $\ell_p$-spaces, that is, $\ell_{\psi}$-spaces, and study their structures.

Article information

Source
Hiroshima Math. J., Volume 37, Number 1 (2007), 1-12.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1176324091

Digital Object Identifier
doi:10.32917/hmj/1176324091

Mathematical Reviews number (MathSciNet)
MR2308520

Zentralblatt MATH identifier
1136.46014

Subjects
Primary: 46B20: Geometry and structure of normed linear spaces

Keywords
Absolute norm strictly convex uniformly convex

Citation

Mitani, Ken-ichi; Saito, Kichi-Suke. On generalized $\bf{\ell_p}$-spaces. Hiroshima Math. J. 37 (2007), no. 1, 1--12. doi:10.32917/hmj/1176324091. https://projecteuclid.org/euclid.hmj/1176324091


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