Honam Mathematical Journal (호남수학학술지)

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A REMARK ON WEAK MODULE-AMENABILITY IN BANACH ALGEBRAS

  • Received : 2020.07.28
  • Accepted : 2021.03.22
  • Published : 2021.06.25
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Abstract

We define a new concept of module amenability which is compatible with original definition of amenability. For a module dual algebra 𝓐, we will show that if every module derivation D : 𝓐** → J𝓐**⊥ is inner then 𝓐 is weak module amenable. Moreover, we will prove that under certain conditions, weak module amenability of 𝓐** implies weak module amenability of 𝓐.

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Acknowledgement

The authors express their sincere thanks to the referee for valuable comments. This article is taken from the second author's dissertation.

References

  1. M. Amini, Module amenability for semigroup algebras, Semigroup fourm, 69, (2004), 302 - 312.
  2. M. Amini and A. Bodaghi, Module amenability and weak module amenability for second dual of Banach algebras, Cham. J. Math. 2 Number 1, (2010), 57 - 71.
  3. W. G. Bade, P. C. Curtis Jr. and H. G. Dales, Amenability and weak amenability for Beurling and Lipschitz algebra, Proc. Lond. Math. Soc. 55. no 3, (1987), 359 - 377.
  4. S. Barootkoob and H. R. Ebrahimi Vishki, Lifting derivations and n-weak amenability of the second dual of a Banach algebra, Bull. Aust. Math. Soc. 83, (2011), 122 - 129. https://doi.org/10.1017/S0004972710001838
  5. J. B. Conway, A course in functional Analysis, Speringer - Verlag, New York, (1985).
  6. H. G. Dales, A. Rodr'iguez-Palacios and M. V. Velasco, The second transpose of a derivation, J. London Math. Soc. 64, (2001), 707 - 721. https://doi.org/10.1112/S0024610701002496
  7. M. Eshaghi Gordji and M. Filali, Weak amenability of the second dual of a Banach algebra, Studia Math, 182 (3), (2007), 205 - 213. https://doi.org/10.4064/sm182-3-2
  8. F. Ghahramani and J. Laali, Amenability and topological center of the second dual of Banach algebras, Bull. Austral. Soc.65, (2002), 191 - 197. https://doi.org/10.1017/S0004972700020232
  9. F. Ghahramani, R. J. Loy and G. A. Willis, Amenability and weak amenability of the second conjugate Banach algebras, Proc. Amer. Math. Soc.124, (1996), 1489 - 1497. https://doi.org/10.1090/s0002-9939-96-03177-2
  10. F. Gourdeau, Amenability and the second dual of a Banach algebra, Studia Math. 125, (1997), 75 - 81. https://doi.org/10.4064/sm-125-1-75-81
  11. B. E. Johnson, Cohomology in Banach algebra, Memoirs Amer. Math. Soc. 127, (1972).