Stability of 2nd conjugate Banach algebras

Open Access
Article
  • 14 Downloads

Abstract

In general the stability of normed algebras is a non hereditary property. We shall prove that second conjugate Banach algebras may be non stable even if the underlying Banach algebra is stable. We shall characterize stability of second conjugate Banach algebras. Finally, we shall study kinds of stability induced on an algebra with an stable second conjugate algebra.

Mathematics Subject Classification

Primary 46H99 Secondary 47B48 

Notes

References

  1. 1.
    Ansari-Piri, E.; Nouri, S.: Almost multipliers and some of their properties. J. Adv. Math. 11(7), 5397–5402 (2015)Google Scholar
  2. 2.
    Ansari-Piri, E.; Nouri, S.: Stable normed algebras. arXiv:1509.08142, 1–8 (2015)
  3. 3.
    Arens, R.: Operations induced in function classes. Monatsh. Math. 55, 1–19 (1951)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Arens, R.: The adjoint of a bilinear operation. Proc. Am. Math. Soc. 2, 839–848 (1951)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Diestel, J.; Uhl, J. J., Jr.: Vector measures. Am. Math. Surveys and Monogr. 15. AMS (1977)Google Scholar
  6. 6.
    Grosser, M.: Arens semi-regularity of the algebra of compact operators. Illinois J. Math. 31(4), 544–573 (1987)MathSciNetMATHGoogle Scholar
  7. 7.
    Palmer, T.W.: Banach algebras and the general theory of *-algebras, vol. I. Cambridge University Press, Cambridge (2004)Google Scholar
  8. 8.
    Palmer, T.W.: The bidual of the compact operators. Trans. Am. Math. Soc. 288(2), 827–839 (1985)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.UNCPBA, FCExactas, Dpto. MatemáticasNUCOMPATandilArgentina

Personalised recommendations