The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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ON χ ⊗ η-STRONG CONNES AMENABILITY OF CERTAIN DUAL BANACH ALGEBRAS

  • Received : 2022.05.24
  • Accepted : 2023.11.09
  • Published : 2024.02.28
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Abstract

In this paper, the notions of strong Connes amenability for certain products of Banach algebras and module extension of dual Banach algebras is investigated. We characterize χ ⊗ η-strong Connes amenability of projective tensor product ${\mathbb{K}}{\hat{\bigotimes}}{\mathbb{H}}$ via χ ⊗ η-σwc virtual diagonals, where χ ∈ 𝕂* and η ∈ ℍ* are linear functionals on dual Banach algebras 𝕂 and ℍ, respectively. Also, we present some conditions for the existence of (χ, θ)-σwc virtual diagonals in the θ-Lau product of 𝕂 ×θ ℍ. Finally, we characterize the notion of (χ, 0)-strong Connes amenability for module extension of dual Banach algebras 𝕂 ⊕ 𝕏, where 𝕏 is a normal Banach 𝕂-bimodule.

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Acknowledgement

The referees have reviewed the paper very carefully. The authors express their deep thanks for the comments.

References

  1. H.R. Ebrahimi Vishki & A.R. Khoddami: Character inner amenability of certain Banach algebras. Colloq. Math. 122 (2011), 225-232. http://eudml.org/doc/283879  https://doi.org/10.4064/cm122-2-7
  2. E.G. Effros: Amenability and virtual diagonals for von Neumann algebras. J. Funct. Anal. 78 (1988), 137-53.  https://doi.org/10.1016/0022-1236(88)90136-X
  3. A. Ghaffari: On character amenability of semigroup algebras. Acta Math. Hungar. 134 (2012), 177-192. https://doi.org/10.1007/s10474-011-0111-5 
  4. A. Ghaffari & S. Javadi: ϕ-Connes amenability of dual Banach algebras. Bull. Iran. Math. Soc. 43 (2017), 25-39. 
  5. A. Ghaffari, S. Javadi & E. Tamimi: ϕ-Connes module amenability of dual Banach algebras. J. of Algebraic Systems 8 (2020), 69-82. DOI: 10.22044/JAS.2019.8503.1415 
  6. A. Ghaffari, S. Javadi & E. Tamimi: Connes amenability of l1-Munn algebras. Tamkang J. of Math. 53 (2022), 259-266. https://doi.org/10.5556/j.tkjm.53.2022.3554 
  7. A. Ghaffari, S. Javadi & E. Tamimi: Connes amenability for certain product of Banach algebras. Wavelet and Linear Algebra 9 (2022), 1-14. DOI: 10.22072/WALA.2021.135909.1301 
  8. B.E. Johnson, R.V. Kadison & J.R. Ringrose: Cohomology of operator algebras. III : reduction to normal cohomology. Bulletin de la S. M. F. 100 (1972), 73-96. 
  9. B.E. Johnson: Symmetric amenability and the nonexistence of Lie and Jordan derivations. Math. Proc. Cambridge Phil. Soc. 120 (1996), 455-473. https://doi.org/10.1017/S0305004100075010 
  10. E. Kaniuth, A.T. Lau & J. Pym: On ϕ-amenability of Banach algebras. Math. Proc. Cambridge Philos. Soc. 144 (2008), 85-96. https://doi.org/10.1017/S0305004107000874 
  11. A. Mahmoodi: On ϕ-Connes amenability of dual Banach algebras. J. Linear. Topological. Algebra 4 (2014), 211-217. 
  12. A. Minapoor & A.Z. Kazempour: Ideal Connes-amenability of certain dual Banach algebras. Complex Anal. Oper. Theory 17 (2023), 17-27. DOI:10.1007/s11785-023-01333-z 
  13. M.S. Monfared: On certain products of Banach algebras with applications to harmonic analysis. Studia Math. 178 (2007), 277-294. DOI:10.4064/sm178-3-4 
  14. V. Runde: Amenability for dual Banach algebras. Studia Math. 148 (2001), 47-66. https://doi.org/10.48550/arXiv.math/0203199 
  15. V. Runde: Connes amenability and normal, virtual diagonals for measure algebras I. J. London Math. Soc. 67 (2003), 643-656. https://doi.org/10.48550/arXiv.math/0111226 
  16. V. Runde: Dual Banach algebras: Connes amenability, normal, virtual diagonals, and injectivity of the predual bimodule. Math. Scand. 1 (2004), 124-144. https://doi.org/10.7146/math.scand.a-14452 
  17. Y. Zhang: Weak amenability of module extension of Banach algebras. Trans. Amer. Math. Soc. 354 (2002), 4131-4151. https://doi.org/10.1090/S0002-9947-02-03039-8