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Uniform structures and square roots in topological groups

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Abstract

Commutative groups uniformly homeomorphic to certain Banach spaces are considered. Results on the relation between the structure of the topological group and the Banach space are obtained.

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References

  1. P. Enflo,Topological groups in which multiplication on one side is differentiable or linear (to appear in Math. Scand.).

  2. P. Enflo,On the non-existence of uniform homeomorphisms between L p -spaces (to appear in Ark. Mat.).

  3. P. Enflo,On a problem of Smirnov (to appear in Ark. Mat.).

  4. I. E. Segal,Topological groups in which multiplication on one side is differentiable. Bull. Amer. Math. Soc.,52 (1946), 481–487.

    Article  MATH  MathSciNet  Google Scholar 

  5. G. Birkhoff,Analytical groups, Trans. Amer. Math. Soc.,43 (1938), 61–101.

    Article  MATH  MathSciNet  Google Scholar 

  6. C. Bessaga,On topological classification of linear metric spaces, Fund. Math.,56 (1965), 251–288.

    MATH  MathSciNet  Google Scholar 

  7. J. Lindenstrauss,On non-linear projections in Banach spaces, Michigan Math. J.,11 (1964), 263–287.

    Article  MATH  MathSciNet  Google Scholar 

  8. J. Kelley,General Topology, van Nostrand, 1955.

  9. D. Montgomery and L. Zippin, Topological Transformation Groups, New York, 1955.

  10. P. Tondeur,Zur Frage der Überdeckbarkeit einer Lieschen Gruppe durch ihre einparametrigen Untergruppen, Math. Ann.,147 (1962), 373–377.

    Article  MATH  MathSciNet  Google Scholar 

  11. A. Malcev,Sur les groupes topologiques locaux et complets, C. R. (Doklady) Acad. Sci., URSS (N.S.),32 (1941), 606–608.

    MathSciNet  Google Scholar 

  12. V. I. Averbukh and O. G. Smolyanov,Theory of differentiation in linear topological spaces, Russian Math. Surveys,22 (1967), 201–258.

    Article  Google Scholar 

  13. J. Dieudonné,Foundations of Modern Analysis, New York, 1960.

  14. M. I. Kadec,A proof of the topological equivalence of all separable infinite-dimensional Banach spaces. (Russian), Funkcional. Anal. i Priloäen.,7 (1967), 61–70.

    MathSciNet  Google Scholar 

  15. S. Mazur,Une remarque sur l’homeomorphie des champs fonctionnels, Studia Math.,1 (1929), 83–85.

    Google Scholar 

  16. G. M. Henkin,Das Fehlen eines gleichmassigen Homömorphismus zwischen räumlichen glatten Funktionen von einer und von n Veränderlichen (n ≧ 2), Mat. Sb. N. S.,74 (116) (1967), 595–607.

    MathSciNet  Google Scholar 

  17. A. Dvoretzky,A characterization of Banach spaces isomorphic to inner product spaces, Proc. Colloquium on Convexity (Copenhagen, 1965), pp. 61–66, Kobenhavns Univ. Mat. Inst., Copenhagen, 1967.

    Google Scholar 

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Authors and Affiliations

  1. Stockholm University, Sweden

    P. Enflo

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  1. P. Enflo
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Enflo, P. Uniform structures and square roots in topological groups. Israel J. Math. 8, 253–272 (1970). https://doi.org/10.1007/BF02771561

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  • DOI: https://doi.org/10.1007/BF02771561

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