Open Access
2015 On some generalized triangle inequalities and $\ell_{\psi}$-spaces
Tamotsu Izumida
Nihonkai Math. J. 26(2): 75-83 (2015).


In this paper, we consider a generalized triangle inequality of the following type: \begin{equation*} \Vert a_1 x_1+\cdots + a_1 x_n \Vert ^p \leq \Vert x_1\Vert^p +\cdots +\Vert x_n\Vert ^p \ (x_1,\ldots, x_n \in X ), \end{equation*} where $(X, \Vert \cdot \Vert)$ is a normed space, $(a_1, \ldots, a_n) \in \Bbb C^n$ and $p>0$. By using generalized $\ell_p$-spaces, we present a characterization of above inequality for infinite sequences $\{x_n\}_{n=1}^{\infty} \subset X$.


Download Citation

Tamotsu Izumida. "On some generalized triangle inequalities and $\ell_{\psi}$-spaces." Nihonkai Math. J. 26 (2) 75 - 83, 2015.


Received: 4 April 2015; Published: 2015
First available in Project Euclid: 12 July 2016

zbMATH: 1352.46023
MathSciNet: MR3521502

Primary: 49J53 , ‎54C60‎
Secondary: 90C29

Keywords: $\psi$-direct sums , ‎absolute norm , generalized $\ell_p$-spaces , Generalized triangle inequality

Rights: Copyright © 2015 Niigata University, Department of Mathematics

Vol.26 • No. 2 • 2015
Back to Top