Some results on approximate character amenability of Banach algebras
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Abstract
In this paper, we prove that two Banach algebras are approximately character amenable if and only if their direct sum is approximately character amenable. Some examples of approximately left character amenable Banach algebras which are not left character amenable are given.
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Bodaghi, A., & Shojaee, B.
(2016).
Some results on approximate character amenability of Banach algebras.
Acta Mathematica Universitatis Comenianae, 85(2), 197-204.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/221/386
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References
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[12] H. Pourmahmood-Aghababa, L. Y. Shi and Y. J. Wu, Generalized Notions of Character Amenability, Acta Mathematica Sinica, English Series, (2013), DOI: 10.1007/s10114-013-0627-4.
[2] H. G. Dales, F. Ghahramani and N. Gronbaek, Derivations into iterated duals of Banach algebras, Studia Math. 128 (1) (1998), 19-54.
[3] F. Ghahramani and R. J. Loy, Generalized notions of amenability, J. Funct. Anal. 208 (2004),229-260.
[4] F. Ghahramani, R. J. Loy and Y. Zhang, Generalized notions of amenability II, J. Funct. Anal. 254 (2008), 1776-1810.
[5] F. Ghahramani, R. J. Loy, and G. A. Willis, Amenability and weak amenability of second conjugate Banach algebras, Proc. Amer. Math. Soc. 124 (1996), 1489-1497.
[6] A. Jabbari, Approximate character amenability of Banach algebras, Stud. Univ. Babes-Bolyai Math., 57, No. 3 (2012), 409-420.
[7] B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972).
[8] E. Kaniuth, A. T. Lau and J. Pym, On \phi-amenability of Banach algebras, Math. Proc. Camb. Phil. Soc. 144 (2008), 85-96.
[9] E. Kaniuth, A. T-M. Lau and J. Pym, On character amenability of Banach algebras, J. Math. Anal. Appl. 344 (2008), 942-955.
[10] M. Sangani-Monfared, Character amenability of Banach algebras, Math. Proc. Camb. Phil. Soc. 144 (2008) 697-706.
[11] V. Runde, Lectures on amenability, Lecture Notes in Mathematics 1774, Springer-Verlage, Berlin, 2002.
[12] H. Pourmahmood-Aghababa, L. Y. Shi and Y. J. Wu, Generalized Notions of Character Amenability, Acta Mathematica Sinica, English Series, (2013), DOI: 10.1007/s10114-013-0627-4.