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

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.