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Dominated extensions of functionals and V-convex functions of cancellative cones

  • S. Romaguera (a1), E. A. Sánchez Pérez (a1) and O. Valero (a1)
Abstract

Let C be a cancellative cone and consider a subcone C0 of C. We study the natural problem of obtaining conditions on a non negative homogeneous function φ: CR+ so that for each linear functional f defined in C0 which is bounded by φ, there exists a linear extension to C. In order to do this we assume several geometric conditions for cones related to the existence of special algebraic basis of the linear span of these cones.

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References
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[1] C. Alegre , J. Ferrer and V. Gregori , ‘On the Hahn-Banach theorem in certain linear quasi-uniform structures’, Acta Math. Hungar. 82 (1999), 315320.

[3] J. Ferrer , V. Gregori and A. Alegre , ‘Quasi-uniform structures in linear lattices’, Rocky Mountain J. Math. 23 (1993), 877884.

[4] L.M. García Raffi , S. Romaguera and E.A. Sánchez Pérez , ‘The bicompletion of an asymmetric normed linear space’, Acta Math. Hungar. 97 (2002), 183191.

[7] L.M. García-Raffi , S. Romaguera and E.A. Sánchez Pérez , ‘Sequence spaces and asymmetric norms in the theory of computational complexity’, Math. Comput. Modelling 36 (2002), 111.

[9] S. Romaguera and M. Sanchis , ‘Semi-Lipschitz functions and best approximation in quasi-metric spaces’, J. Approx. Theory 103 (2000), 292301.

[10] S. Romaguera and M. Schellekens , ‘Quasi-metric properties of complexity spaces’, Topology Appl. 98 (1999), 311322.

[13] R. Tix , ‘Some results on Hahn-Banach type theorems for continuous d-cones’, Theoret. Comput. Sci. 264 (2001), 205218.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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