Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T01:16:56.956Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  17 April 2009

S. Romaguera ,
E. A. Sánchez Pérez  and
O. Valero
S. Romaguera
Affiliation:
Escuela de Caminos, Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, 46071 Valencia, Spain, e-mail: [email protected], [email protected], [email protected]
E. A. Sánchez Pérez
Affiliation:
Escuela de Caminos, Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, 46071 Valencia, Spain, e-mail: [email protected], [email protected], [email protected]
O. Valero
Affiliation:
Escuela de Caminos, Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, 46071 Valencia, Spain, e-mail: [email protected], [email protected], [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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: C → R+ 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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 1 , February 2003 , pp. 87 - 94
Copyright
Copyright © Australian Mathematical Society 2003

References

REFERENCES

[1]Alegre, C., Ferrer, J. and Gregori, V., ‘On the Hahn-Banach theorem in certain linear quasi-uniform structures’, Acta Math. Hungar. 82 (1999), 315–320.CrossRefGoogle Scholar
[2]Fuchssteiner, B. and Lusky, W., Convex cones (North-Holland Publishing Co., Amsterdam, 1981).Google Scholar
[3]Ferrer, J., Gregori, V. and Alegre, A., ‘Quasi-uniform structures in linear lattices’, Rocky Mountain J. Math. 23 (1993), 877–884.CrossRefGoogle Scholar
[4]Raffi, L.M. García, Romaguera, S. and Pérez, E.A. Sánchez, ‘The bicompletion of an asymmetric normed linear space’, Acta Math. Hungar. 97 (2002), 183–191.CrossRefGoogle Scholar
[5]Raffi, L.M. García, Romaguera, S. and Pérez, E.A. Sánchez, ‘On Hausdorff asymmetric normed linear spaces’, Houston J. of Math. (to appear).Google Scholar
[6]Raffi, L.M. García, Romaguera, S. and Pérez, E.A. Sánchez, ‘Extensions of asymmetric norms to linear spaces’, Rend. Istit. Mat. Univ. Trieste. 33 (2001), 113–125.Google Scholar
[7]García-Raffi, L.M., Romaguera, S. and Pérez, E.A. Sánchez, ‘Sequence spaces and asymmetric norms in the theory of computational complexity’, Math. Comput. Modelling 36 (2002), 1–11.CrossRefGoogle Scholar
[8]Hungerford, T.W., Algebra, Graduate Texts in Mathematics 73 (Springer-Verlag, Berlin, Heidelberg, New York, 1974).Google Scholar
[9]Romaguera, S. and Sanchis, M., ‘Semi-Lipschitz functions and best approximation in quasi-metric spaces’, J. Approx. Theory 103 (2000), 292–301.CrossRefGoogle Scholar
[10]Romaguera, S. and Schellekens, M., ‘Quasi-metric properties of complexity spaces’, Topology Appl. 98 (1999), 311–322.CrossRefGoogle Scholar
[11]Roth, W., ‘Hahn-Banach type theorems for locally convex cones’, J. Austral. Math. Soc. Ser. A 68 (2000), 104–125.CrossRefGoogle Scholar
[12]Rudin, W., Functional analysis (McGraw-Hill Publishing Co., New York, Dusseldorf, Johannesburg, 1973).Google Scholar
[13]Tix, R., ‘Some results on Hahn-Banach type theorems for continuous d-cones’, Theoret. Comput. Sci. 264 (2001), 205–218.CrossRefGoogle Scholar