Acta Mathematica Sinica, English Series

, Volume 23, Issue 6, pp 1067–1074

A Characterization of Generalized Monotone Normed Cones

ORIGINAL ARTICLES

DOI: 10.1007/s10114-005-0799-7

Cite this article as:
Romaguera, S., Sánchez-Pérez, E.A. & Valero, O. Acta Math Sinica (2007) 23: 1067. doi:10.1007/s10114-005-0799-7

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.

Keywords

quasi–norm monotone cones 

MR (2000) Subject Classification

54E50 54H99 43D35 

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • S. Romaguera
    • 1
  • E. A. Sánchez-Pérez
    • 1
  • O. Valero
    • 2
  1. 1.Escuela de Caminos, Departamento de Matemática AplicadaUniversidad Politécnica de ValenciaValenciaSpain
  2. 2.Departamento de Ciencias Matématicas e InformáticaUniversidad de las Islas Baleares, Edificio Anselm TurmedaPalma, BalearesSpain