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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.

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Authors and Affiliations

  1. Escuela de Caminos, Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, 46071, Valencia, Spain

    S. Romaguera & E. A. Sánchez-Pérez

  2. Departamento de Ciencias Matématicas e Informática, Universidad de las Islas Baleares, Edificio Anselm Turmeda, 07122, Palma, Baleares, Spain

    O. Valero

Authors
  1. S. Romaguera
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  2. E. A. Sánchez-Pérez
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  3. O. Valero
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Correspondence to S. Romaguera.

Additional information

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

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Romaguera, S., Sánchez-Pérez, E.A. & Valero, O. A Characterization of Generalized Monotone Normed Cones. Acta Math Sinica 23, 1067–1074 (2007). https://doi.org/10.1007/s10114-005-0799-7

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  • DOI: https://doi.org/10.1007/s10114-005-0799-7

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