Metrizability of the unit ball of the dual of a quasi-normed cone
García-Raffi, L. M. ; Romaguera, S. ; Sánchez-Pérez, E. A. ; Valero, O.
Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004), p. 483-492 / Harvested from Biblioteca Digitale Italiana di Matematica
Access to full text
Full (PDF)
Full (DjVu)

We obtain theorems of metrization and quasi-metrization for several topologies of weak* type on the unit ball of the dual of any separable quasi-normed cone. This is done with the help of an appropriate version of the Alaoglu theorem which is also obtained here.

Dimostriamo teoremi di metrizzabilità e di quasi metrizzabilità per alcune topologie di tipo debole* sulla palla unitaria del duale di un cono quasi normato separabile. Ciò è ottenuto grazie a un'opportuna versione del teorema di Alaoglu, anch'essa dimostrata nel presente lavoro.

Publié le : 2004-06-01
@article{BUMI_2004_8_7B_2_483_0,
     author = {L. M. Garc\'\i a-Raffi and S. Romaguera and E. A. S\'anchez-P\'erez and O. Valero},
     title = {Metrizability of the unit ball of the dual of a quasi-normed cone},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {7-A},
     year = {2004},
     pages = {483-492},
     zbl = {1116.46009},
     mrnumber = {2072949},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2004_8_7B_2_483_0}
}

García-Raffi, L. M.; Romaguera, S.; Sánchez-Pérez, E. A.; Valero, O. Metrizability of the unit ball of the dual of a quasi-normed cone. Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004) pp. 483-492. http://gdmltest.u-ga.fr/item/BUMI_2004_8_7B_2_483_0/

[1] Alimov, A. R., On the structure of the complements of Chebyshev sets, Funct. Anal. Appl., 35 (2001), 176-182. | MR 1864985 | Zbl 1099.41501

[2] Dolzhenko, E. P.-Sevast'Yanov, E. A., Sign-sensitive approximations, the space of sign-sensitive weights. The rigidity and the freedom of a system, Russian Acad. Sci. Dokl. Math., 48 (1994), 397-401. | MR 1272960 | Zbl 0818.41028

[3] Fletcher, P.-Lindgren, W. F., Quasi-Uniform Spaces, Marcel Dekker, 1982. | MR 660063 | Zbl 0501.54018

[4] García-Raffi, L. M.-Romaguera, S.-Sánchez-Pérez, E. A., Sequence spaces and asymmetric norms in the theory of computational complexity, Math. Comput. Model., 36 (2002), 1-11. | MR 1925055 | Zbl 1063.68057

[5] García-Raffi, L. M.-Romaguera, S.-Sánchez-Pérez, E. A., The dual space of an asymmetric normed linear space, Quaestiones Math., 26 (2003), 83-96. | MR 1974407 | Zbl 1043.46021

[6] Keimel, K.-Roth, W., Ordered Cones and Approximation, Springer-Verlag, Berlin, 1992. | MR 1176514 | Zbl 0752.41033

[7] Kopperman, R., Lengths on semigroups and groups, Semigroup Forum, 25 (1982), 345-360. | MR 679288 | Zbl 0502.22002

[8] Künzi, H. P. A., Nonsymmetric distances and their associated topologies: About the origins of basic ideas in the area of asymmetric topology, in: Handbook of the History of General Topology, C. E. Aull and R. Lowen (eds), Kluwer Acad. Publ., 3 (2001), 853-968. | MR 1900267 | Zbl 1002.54002

[9] Romaguera, S.-Sánchez-Pérez, E. A.-Valero, O., Quasi-normed monoids and quasi-metrics, Publ. Math. Debrecen, 62 (2003), 53-69. | MR 1956801 | Zbl 1026.54027

[10] Romaguera, S.-Sanchis, M., Semi-Lipschitz functions and best approximation in quasi-metric spaces, J. Approx. Theory, 103 (2000), 292-301. | MR 1749967 | Zbl 0980.41029

[11] Romaguera, S.-Schellekens, M., Duality and quasi-normability for complexity spaces, Appl. Gen. Topology, 3 (2002), 91-112. | MR 1931256 | Zbl 1022.54018

[12] Tix, R., Some results on Hahn-Banach-type theorems for continuous D-cones, Theoretical Comput. Sci., 264 (2001), 205-218. | MR 1857456 | Zbl 0973.68123

[13] Wojtaszczyk, P., Banach Spaces for Analysts, Cambridge Univ. Press, Cambridge, 1991. | MR 1144277 | Zbl 0724.46012