Ir al contenido

Documat


Unitary representability of free abelian topological groups

  • Uspenskij, Vladimir V. [1]
    1. [1] Ohio University

      Ohio University

      Township of Athens, Estados Unidos

  • Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 9, Nº. 2, 2008, págs. 197-204
  • Idioma: inglés
  • DOI: 10.4995/agt.2008.1800
  • Enlaces
  • Resumen
    • For every Tikhonov space X the free abelian topological group A(X) and the free locally convex vector space L(X) admit a topologically faithful unitary representation. For compact spaces X this is due to Jorge Galindo.

  • Referencias bibliográficas
    • W. Banaszczyk, On the existence of exotic Banach – Lie groups, Math. Ann. 264 (1983), 485–493.
    • http://dx.doi.org/10.1007/BF01456956
    • B. Bekka, P. de la Harpe, and A. Valette, Kazhdan property (T), available at http://poncelet.sciences.univ-metz.fr/˜bekka/.
    • Y. Benyamini and J. Lindenstrauss, Geometric nonlinear functional analysis, Vol. 1, AMS Colloquium Publications, vol. 48 (AMS, Providence,...
    • J. Galindo, On unitary representability of topological groups, arXiv:math.GN/0607193.
    • S. Gao and V. Pestov, On a universality property of some abelian Polish groups, Fund. Math. 179 (2003), 1–15; arXiv:math.GN/0205291.
    • M. Megrelishvili, Reflexively but not unitarily representable topological groups, Topology Proceedings 25 (2000), 615–625.
    • E. Michael, Continuous selections I, Ann. Math. 63 (1956), 361–382.
    • http://dx.doi.org/10.2307/1969615
    • V. Pestov, Dynamics of infinite-dimensional groups and Ramsey-type phenomena, (Publica¸c˜oes dos Colóquios de Matemática, IMPA, Rio de Janeiro,...
    • V. Pestov, Forty-plus annotated questions about large topological groups, arXiv:math.GN/0512564.
    • I. J. Shoenberg, On certain metric spaces arising from Euclidean spaces by a change of metric and their imbedding in Hilbert space, Ann. Math....
    • http://dx.doi.org/10.2307/1968835
    • I. J. Schoenberg, Metric spaces and positive definite functions, Trans. Amer. Math. Soc. 44 (1938), 522–536.
    • http://dx.doi.org/10.1090/S0002-9947-1938-1501980-0
    • M. G. Tkachenko, On completeness of free abelian topological groups, Soviet Math. Dokl. 27 (1983), 341–345.
    • D. Repovˇs and P. V. Semenov, Continuous selections of multivalued mappings, Kluwer Academic Publishers, Dordrecht–Boston–London, 1998.
    • V. V. Uspenskii, Why compact groups are dyadic, in book: General Topology and its relations to modern analysis and algebra VI: Proc. of the...
    • V. V. Uspenski˘ı, Free topological groups of metrizable spaces, Izvestiya Akad. Nauk SSSR, Ser. Matem. 54 (1990), 1295–1319; English transl.:...
    • http://dx.doi.org/10.1070/IM1991v037n03ABEH002163
    • V. V. Uspenskij, On unitary representations of groups of isometries, in book: Contribuciones Matem´aticas. Homenaje al profesor Enrique Outerelo...

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno