Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SOME CHARACTERIZATIONS OF CHARACTER AMENABLE BANACH ALGEBRAS

  • Received : 2013.11.24
  • Published : 2015.05.31
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Abstract

In this study, the character amenability of Banach algebras is considered and some characterization theorems are established. Indeed, we prove that the character amenability of Lipschitz algebras is equivalent to that of Banach algebras.

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References

  1. M. Abtahi and Y. Zhang, A new proof of the amenability of C(X), Bull. Aust. Math. Soc. 81 (2010), no. 3, 414-417. https://doi.org/10.1017/S0004972709001063
  2. M. Alaghmandian, R. Nasr-Isfahani, and M. Nemati, Character amenability and con- tractibility of abstract Segal algebras, Bull. Aust. Math. Soc. 82 (2010), no. 2, 274-281. https://doi.org/10.1017/S0004972710000286
  3. W. G. Bade, P. C. Curtis, and H. G. Dales, Amenability and weak amenability for Beurling and Lipschitz algebras, Proc. London Math. Soc. 55 (1987), no. 2, 359-377.
  4. M. Dashti, R. Nasr-Isfahani, and S. Soltani Renani, Character Amenability of Lipschitz Algebras, Canad. Math. Bull. 57 (2014), no. 1, 37-41. https://doi.org/10.4153/CMB-2012-015-3
  5. A. Ghaffari, On character amenability of semigroup algebras, Acta Math. Hungar. 134 (2012), no. 1-2, 177-192. https://doi.org/10.1007/s10474-011-0111-5
  6. F. Ghahramani and R. J. Loy, Generalized notion of amenability, J. Funct. Anal. 208 (2004), no. 1, 229-260. https://doi.org/10.1016/S0022-1236(03)00214-3
  7. F. Gourdeau, Amenability of Banach algebras, Math. Proc. Cambridge Phil. Soc. 105 (1989), no. 2, 351-356. https://doi.org/10.1017/S0305004100067840
  8. F. Gourdeau, Amenability of Lipschitz algebras, Math. Proc. Cambridge Phil. Soc. 112 (1992), no. 3, 581-588. https://doi.org/10.1017/S0305004100071267
  9. N. Gronbaek, Amenability and weak amenability of tensor algebras and algebras of nuclear operators, J. Aust. Math. Soc. 51 (1991), no. 3, 483-488. https://doi.org/10.1017/S1446788700034649
  10. A. Ya. Helemskii, Banach and Locally Convex Algebras, Oxford University Press, Oxford, 1993.
  11. Z. Hu, M. Sangani Monfared, and T. Traynor, On character amenable Banach algebras, Studia Math. 193 (2008), no. 1, 53-78. https://doi.org/10.4064/sm193-1-3
  12. B. E. Johnson, Cohomology in Banach algebras, Memoirs of the American Mathematical Society, No. 127. American Mathematical Society, Providence, R.I., 1972.
  13. E. Kaniuth, A. T. Lau, and J. Pym, On $\varphi$-amenability of Banach algebras, Math. Proc. Camb. Phil. Soc. 144 (2008), no. 1, 85-96. https://doi.org/10.1017/S0305004107000874
  14. E. Kaniuth, A. T. Lau, and J. Pym, On character amenability of Banach algebras, J. Math. Anal. Appl. 344 (2008), no. 2, 942-955. https://doi.org/10.1016/j.jmaa.2008.03.037
  15. A. T.-M. Lau, Characterization of amenable Banach algebras, Proc. Amer. Math. Soc. 70 (1978), 156-160.
  16. A. T.-M. Lau, Analysis on a class of Banach algebras with application to harmonic analysison locally compact groups and semigroups, Fund. Math. 118 (1983), 161-175.
  17. A. T.-M. Lau and Y. Zhang, Finite dimensional invariant subspace property and amenability for a class of Banach algebras, Trans. Amer. Math. Soc., to appear
  18. M. S. Monfared, Character amenability of Banach algebras, Math. Proc. Cambrigde Phil. Soc. 144 (2008), no. 3, 697-706. https://doi.org/10.1017/S0305004108001126
  19. R. Nasr-Isfahani and M. Nemati, Essential character amenability of Banach algebras, Bull. Aust. Math. Soc. 84 (2011), no. 3, 372-386. https://doi.org/10.1017/S0004972711002620
  20. D. R. Sherbert, The structure of ideals and point derivations in Banach algebras of Lipschitz functions, Trans. Amer. Math. Soc. 111 (1964), 240-272. https://doi.org/10.1090/S0002-9947-1964-0161177-1
  21. N. Weaver, Lipschitz Algebras, World Scientific Publishing Co. Pte Ltd., 1999.