, Volume 23, Issue 6, pp 1067-1074
Date: 18 Jun 2006

A Characterization of Generalized Monotone Normed Cones

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Abstract

Let C be a cone and consider a quasi–norm p defined on it. We study the structure of the couple (C, p) as a topological space in the case where the function p is also monotone. We characterize when the topology of a quasi–normed cone can be defined by means of a monotone norm. We also define and study the dual cone of a monotone normed cone and the monotone quotient of a general cone. We provide a decomposition theorem which allows us to write a cone as a direct sum of a monotone subcone that is isomorphic to the monotone quotient and other particular subcone.

The authors acknowledge the support of the Spanish Ministry of Science and Technology and FEDER under Grant BFM2003–02302