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Numerical representation of topological real algebras
Representación numérica de álgebras reales topológicas
DOI :
https://doi.org/10.15446/recolma.v57n1.112429Mots-clés :
Gelfand-Mazur's theorem, Real algebra, Continuous numerical representations of total pre-orders (en)Teorema de Gelfand-Mazur, álgebra real, representaciones reales continuas numéricas de preóordenes (es)
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We show that the isomorphism provided by the Gelfand-Mazur theorem for a commutative pre-ordered real Banach algebra A with unit defines a numerical representation which is compatible with the order structure.
Utilizamos que el isomorfismo dado por el teorema de Gelfand-Mazur para álgebras reales de Banach reales preordenadas conmutativas con unidad a su vez define una representación numérica compatible con la estructura de orden.
Références
F. Albiac and E. Briem, Representations of real Banach algebras, J. Aust. Math. Soc. 88 (2010), 289-300. DOI: https://doi.org/10.1017/S144678871000011X
M. J. Campión, J. C. Candeal, and E. Induráin, The existence of utility functions for weakly continuous preferences on a Banach space, Math. Social Sci. 51 (2006), no. 2, 227-237. DOI: https://doi.org/10.1016/j.mathsocsci.2005.07.007
J. C. Candeal, The continuous representability property in algebraic systems, In: Valero, O., Rodriguez-López, J., Tirado, P. (ed.) Applied Topology: Recent progress for computer science, fuzzy mathematics and economics WiAT'09 Conference Proceedings, 2009.
J. C. Candeal, E. Induráin, and J. A. Molina, Numerical representability of ordered topological spaces with compatible algebraic structure, Order 29 (2012), 131-146, DOI 10.1007/s11083-011-9202-8. DOI: https://doi.org/10.1007/s11083-011-9202-8
J. C. Candeal, J. R. De Miguel, and E. Induráin, Universal semigroups in additive utility, Semigroup Forum 56 (1998), 288-296. DOI: https://doi.org/10.1007/PL00005947
L. Inglestam, Real Banach algebras, Ark. Mat. 5 (1964), 239-270. DOI: https://doi.org/10.1007/BF02591126
I. Kaplansky, Normed algebras, Duke Math. J. 16 (1949), 399-418. DOI: https://doi.org/10.1215/S0012-7094-49-01640-3
M. Oudadess, Theorem of Gelfand-Mazur and commutativity in unital real topological algebras, Mediterr. J. Math. 8 (2010), 137-151. DOI: https://doi.org/10.1007/s00009-010-0092-6
H. Raubenheimer and S. Rode, Cones in Banach algebras, Indag. Mathem., N.S. 7 (1996), no. 4, 489-502. DOI: https://doi.org/10.1016/S0019-3577(97)89135-5
