DOI QR코드

DOI QR Code

The Hahn-Banach Theorem on Arbitrary Groups

  • Huang, Jianfeng (Department of Mathematics, Sun Yat-Sen University) ;
  • Li, Yongjin (Department of Mathematics, Sun Yat-Sen University)
  • Received : 2007.12.18
  • Accepted : 2008.08.15
  • Published : 2009.06.30

Abstract

In this paper, one kind of subgroup in arbitrary group which similar to the linear subspace was constructed, and the generalization of the Hahn-Banach theorem on this kind of subgroup in arbitrary groups was obtained.

Keywords

References

  1. R. Badora, On the Hahn-Banach theorem for groups, Arch. Math., 86(2006), 517-528. https://doi.org/10.1007/s00013-005-1570-0
  2. G. Buskes, The Hahn-Banach theorem surveyed, Dissertationes Math. (Rozprawy Mat.), 327(1993), 49 pp.
  3. Z. Gajda, Z. Kominek, On separation theorems for subadditive and superadditive functionals, Studia Math., 100(1991), 25-38. https://doi.org/10.4064/sm-100-1-25-38
  4. D. H. Hyers, G. Isac and T. M. Rassias, Stability of functional equations in several variables, Progress in Nonlinear Differential Equations and their Applications, 34. Birkhauser Boston, Inc., Boston, MA, 1998.
  5. A. Chaljub-Simon, P. Volkmann, Bemerkungen zu einem Satz von Rode. (German) Arch. Math. (Basel), 57(1991), 180-188. https://doi.org/10.1007/BF01190005
  6. R. J. Silverman, Means on Semigroups and the Hahn-Banach Extension Property, Trans. Amer. Math. Soc., 83(1956), 222-237. https://doi.org/10.1090/S0002-9947-1956-0084721-7
  7. J. Tabor, Remark 18, Report of Meeting, the 22nd Internat Symposium on functional Equations, Aequationes. Math., 29(1985), 96.
  8. R. Ged, Fischer-Muszely additivity on abelian groups, Comment. Math. Prace Mat., 2004, Tomus specialis in Honorem Juliani Musielak, 82-96.