Weakly compact homomorphisms of regular Banach algebras



Let A be a uniformly regular Ditkin algebra. It is shown that every weakly compact homomorphism of A into a Banach algebra is finite-dimensional.

Key words

Banach algebra group algebra homomorphism 


  1. 1]
    I. Gelfand, D. Raikov, and G. Shilov, Commutative Normed Rings, Chelsea Publ. Comp., 1964.Google Scholar
  2. [2]
    E. A. Gorin, Uspekhi Mat. Nauk, 33:4 (1978), 169–188; English transl.: Russian Math. Surveys, 33:4 (1978), 193–217.MATHMathSciNetGoogle Scholar
  3. [3]
    K. B. Laursen and M. Neumann, An Introduction to Local Spectral Theory, The Clarendon Press, Oxford Univ. Press, 2000.Google Scholar
  4. [4]
    A. Ülger, Studia Math., 153:1 (2002), 59–80.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    E. Hewitt and K. Ross, Abstract Harmonic Analysis II, Springer-Verlag, New York-Berlin, 1970.MATHGoogle Scholar
  6. [6]
    C. Herz, Ann. Inst. Fourier, 23 (1973), 91–123.MATHMathSciNetGoogle Scholar
  7. [7]
    M. Leinert, Studia Math., 52 (1974), 149–158.MathSciNetGoogle Scholar
  8. [8]
    C. Rickart, General Theory of Banach Algebras, Van Nostrand, Princeton, NJ, 1960.MATHGoogle Scholar
  9. [9]
    E. E. Granirer, Math. Japonica, 46:1 (1997), 69–72.MATHMathSciNetGoogle Scholar
  10. [10]
    A. Ülger, Monatsh. Math., 121:4 (1996), 353–379.MATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    J. E. Gale, T. J. Ransford, and M. C. White, Trans. Amer. Math. Soc., 331:2 (1992), 815–824.MATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    E. E. Granirer, Colloq. Math., 51 (1987), 155–163.MATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Faculty of Arts and Sciences, Department of MathematicsYuzuncu Yil UniversityTurkey

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