SOME CHARACTERIZATIONS OF CHARACTER AMENABLE BANACH ALGEBRAS

Title & Authors
SOME CHARACTERIZATIONS OF CHARACTER AMENABLE BANACH ALGEBRAS
Gordji, Madjid Eshaghi; Jabbari, Ali; Kim, Gwang Hui;

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.
Keywords
amenability;Banach algebra;character amenability;
Language
English
Cited by
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.

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.

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.

5.
A. Ghaffari, On character amenability of semigroup algebras, Acta Math. Hungar. 134 (2012), no. 1-2, 177-192.

6.
F. Ghahramani and R. J. Loy, Generalized notion of amenability, J. Funct. Anal. 208 (2004), no. 1, 229-260.

7.
F. Gourdeau, Amenability of Banach algebras, Math. Proc. Cambridge Phil. Soc. 105 (1989), no. 2, 351-356.

8.
F. Gourdeau, Amenability of Lipschitz algebras, Math. Proc. Cambridge Phil. Soc. 112 (1992), no. 3, 581-588.

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.

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.

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.

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.

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.

19.
R. Nasr-Isfahani and M. Nemati, Essential character amenability of Banach algebras, Bull. Aust. Math. Soc. 84 (2011), no. 3, 372-386.

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.

21.
N. Weaver, Lipschitz Algebras, World Scientific Publishing Co. Pte Ltd., 1999.