Generalized M-norms on ordered normed spaces

• Autorzy: I. Tzschichholtz , M. R. Weber
• 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.

Kategorie tematyczne

• 46A40: Ordered topological linear spaces, vector lattices
• 46A20: Duality theory
• 46B40: Ordered normed spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2005
• Tom: 68
• Numer: 1
• Strony: 115-123

Daty

wydano

2005

Twórcy

autor

I. Tzschichholtz

• Institute of Analysis, Technische Universität Dresden, Dresden, Germany

autor

M. R. Weber

• Institute of Analysis, Technische Universität Dresden, Dresden, Germany

Identyfikatory

DOI

10.4064/bc68-0-14