PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

## Banach Center Publications

2005 | 68 | 1 | 115-123
Tytuł artykułu

### Generalized M-norms on ordered normed spaces

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
115-123
Opis fizyczny
Daty
wydano
2005
Twórcy
autor
• Institute of Analysis, Technische Universität Dresden, Dresden, Germany
autor
• Institute of Analysis, Technische Universität Dresden, Dresden, Germany
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory