# Generalized M-norms on ordered normed spaces

Banach Center Publications (2005)

- Volume: 68, Issue: 1, page 115-123
- ISSN: 0137-6934

## Access Full Article

top## Abstract

top## How to cite

topI. Tzschichholtz, and M. R. Weber. "Generalized M-norms on ordered normed spaces." Banach Center Publications 68.1 (2005): 115-123. <http://eudml.org/doc/282299>.

@article{I2005,

abstract = {L-norms and M-norms on Banach lattices, unit-norms and base norms on ordered vector spaces are well known. In this paper m- and $m_\{≤\}$-norms are introduced on ordered normed spaces. They generalize the notions of the M-norm and the order-unit norm, possess also some interesting properties and can be characterized by means of the constants of reproducibility of cones. In particular, the dual norm of an ordered Banach space with a closed cone turns out to be additive on the dual cone if and only if the norm of the Banach space is an $m_\{≤\}$-norm and, on the other hand, the norm of an ordered normed space with a reproducing cone is an L-norm if and only if the dual norm is an $m_\{≤\}$-norm. Conditions are given for the operator norm to be an $m_\{≤\}$- or an L-norm.},

author = {I. Tzschichholtz, M. R. Weber},

journal = {Banach Center Publications},

language = {eng},

number = {1},

pages = {115-123},

title = {Generalized M-norms on ordered normed spaces},

url = {http://eudml.org/doc/282299},

volume = {68},

year = {2005},

}

TY - JOUR

AU - I. Tzschichholtz

AU - M. R. Weber

TI - Generalized M-norms on ordered normed spaces

JO - Banach Center Publications

PY - 2005

VL - 68

IS - 1

SP - 115

EP - 123

AB - L-norms and M-norms on Banach lattices, unit-norms and base norms on ordered vector spaces are well known. In this paper m- and $m_{≤}$-norms are introduced on ordered normed spaces. They generalize the notions of the M-norm and the order-unit norm, possess also some interesting properties and can be characterized by means of the constants of reproducibility of cones. In particular, the dual norm of an ordered Banach space with a closed cone turns out to be additive on the dual cone if and only if the norm of the Banach space is an $m_{≤}$-norm and, on the other hand, the norm of an ordered normed space with a reproducing cone is an L-norm if and only if the dual norm is an $m_{≤}$-norm. Conditions are given for the operator norm to be an $m_{≤}$- or an L-norm.

LA - eng

UR - http://eudml.org/doc/282299

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.