Group topologies on vector spaces and character lifting properties

• Autores: Xabier Domínguez , Vaja Tarieladze
• Localización: Boletín de la Sociedad Matemática Mexicana: Tercera Serie, ISSN 1405-213X, ISSN-e 2296-4495, Vol. 14, Nº. 1, 2008, págs. 21-34
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • It is known that every continuous character on a topological vector space can be lifted to a continuous linear functional and, moreover, these liftings give rise to a topological isomorphism between the dual group and the dual space, when both are endowed with the compact-open topology. We investigate the presence of these properties in more general topologized real vector spaces.

• Referencias bibliográficas
  • L. AußENHOFER, Contributions to the duality theory ofAbelian topological groups and to the theory of nuclear groups, Dissertationes Math....
  • W. BANASZCZYK, Additive subgroups of topological vector spaces. Lecture Notes in Mathematics, 1466, Springer-Verlag, Berlin-Heidelberg, 1991.
  • N. BOURBAKl, Éléments de mathématique: Espaces vectoriels topologiques, Masson, Paris, 1981.
  • M. J. CHASCO, E. MARTÍN-PEINADOR, V. TARIELADZE, On Mackey topology for groups, Studia Math. 132 (3), (1999), 257-284.
  • V. M. DERGAČEV, O topologičeskih vektornyh gruppah. Uspekhi Mat. Nauk 33 (4) (1978), 209-210. (English translation: Topological vector groups,...
  • D. DIKRANJAN, P. PRODANOV, L. STOYANOV, Topological groups. Characters, dualities and minimal group topologies, Monographs and Textbooks in...
  • X. DOMÍNGUEZ, Grupos abelianos topológicos y sumabilidad, Doctoral dissertation (Spanish), Univ. Complutense de Madrid, 2002, URL: http :...
  • X. DOMÍNGUEZ, V. TARIELADZE, GP-nuclear groups, Research Exposition in Mathematics 24 (2000), 127-161.
  • P. FLOR, Zur Bohr-Konvergenz von Folgen, Math. Scand. 23 (1968), 169-170.
  • I. GLICKSBERG, Uniform boundedness for groups, Cañad. J. Math. 14 (1962), 269-276.
  • P. KENDEROV, On topological vector groups, Mat. Sb. (N.S.) 81 (123) (1970), no. 4, 580-599. (Russian.)(English translation: Math. USSR Sb.,...
  • G. HAMEL, Eine Basis aller Zahlen und die unstetigen Lösungen der Funktionalgleichung: f(x+y) = f(x) + f(y). Math. Ann. 60 (1905),...
  • E. HEWITT, K. A. ROSS, Abstract Harmonie Analysis I. Grundlehren der mathematischen Wissenschaften, 115, Springer-Verlag. Berlin, Heidelberg,...
  • E. HEWITT, H. S. ZUCKERMANN, A group-theoretic method in approximation theory, Ann. of Math. 52 (2), (1950), 557-567.
  • S. A. MORRIS, Pontryagin duality and the structure of locally compact groups, Cambridge University Press, Cambridge London, New York Melb...
  • I. MUNTEAN, Sur la non-trivialité du dual des groupes vectoriels topologiques, Mathematica (Cluj) 14 (37) (1972), 259-262.
  • J. W. NIENHUYS, A solenoidal and monothetic minimally almost periodic group, Fund. Math. 73 (2), (1971/72), 167-169.
  • P. NICKOLAS, Reflexivity of topological groups, Proc. Amer. Math. Soc. 65 (1), (1977), 137-141.
  • D. A. RAǏKOV, On B-complete topological vector groups, (Russian) Studia Math. 31 (1968), 295-306.
  • M. F. SMITH, The Pontrjagin theorem in linear spaces, Ann. of Math. 56 (2), (1952), 248-253.
  • M. STROPPEL, Locally compact groups. EMS Texts in Mathematics. European Mathematical Society, 2006.
  • S. WARNER, Topological Fields. North-Holland Mathematics Studies, 157. North-Holland, 1989.