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Character Amenability of Lipschitz Algebras

Published online by Cambridge University Press:  20 November 2018

Mahshid Dashti ,
Rasoul Nasr-Isfahani  and
Sima Soltani Renani
Mahshid Dashti
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran e-mail: [email protected]@[email protected]
Rasoul Nasr-Isfahani
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran e-mail: [email protected]@[email protected]
Sima Soltani Renani
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran e-mail: [email protected]@[email protected]
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Abstract

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Let $\chi $ be a locally compact metric space and let $\mathcal{A}$ be any of the Lipschitz algebras $\text{Li}{{\text{p}}_{\alpha }}\text{ }\!\!\chi\!\!\text{ }$, $\text{Li}{{\text{p}}_{\alpha }}\text{ }\!\!\chi\!\!\text{ }$, or $\text{lip}_{\alpha }^{0}\,\chi $. In this paper, we show, as a consequence of rather more general results on Banach algebras, that $\mathcal{A}$ is $C$-character amenable if and only if $\chi $ is uniformly discrete.

Keywords

43A0746H0546J10character amenablecharacter contractibleLipschitz algebrasspectrum
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 1 , 14 March 2014 , pp. 37 - 41
Copyright
Copyright © Canadian Mathematical Society 2014

References

[1] Bade, W. G., Curtis, P. C. Jr., and Dales, H. G., Amenability and weak amenability for Beurling andLipschitz algebras. Proc. London Math. Soc. 55 (1987), no. 2, 359–377. http://dx.doi.org/10.1093/plms/s3-55 2.359 Google Scholar
[2] Bishop, E. R., Generalized Lipschitz algebras. Canad. Math. Bull. 12 (1969), 1–19. http://dx.doi.org/10.4153/CMB-1969-001-2 Google Scholar
[3] Gourdeau, F., Amenability of Banach algebras. Math. Proc. Cambridge Philos. Soc. 105 (1989), no. 2, 351–355. http://dx.doi.org/10.1017/S0305004100067840 Google Scholar
[4] Gourdeau, F., Amenability of Lipschitz algebras. Math. Proc. Cambridge Philos. Soc. 112 (1992), no. 3, 581–588. http://dx.doi.org/10.1017/S0305004100071267 Google Scholar
[5] Hu, Z., Monfared, M. S., and Traynor, T., On character amenable Banach algebras. Studia Math. 193 (2009), no. 1, 53–78. http://dx.doi.org/10.4064/sm193-1-3 Google Scholar
[6] Johnson, B. E., Cohomology in Banach algebras. Memoirs of the American Mathematical Society, 127, American Mathematical Society, Providence, RI, 1972.Google Scholar
[7] Kaniuth, E., Lau, A. T., and Pym, J., On -amenability of Banach algebras. Math. Proc. Cambridge Philos. Soc. 144 (2008), no. 1, 85–96.Google Scholar
[8] Kaniuth, E., Lau, A. T., and Pym, J., On character amenability of Banach algebras. J. Math. Anal. Appl. 344 (2008), no. 2, 942–955. http://dx.doi.org/10.1016/j.jmaa.2008.03.037 Google Scholar
[9] Monfared, M. S., Character amenability of Banach algebras. Math. Proc. Cambridge Philos. Soc. 144 (2008), no. 3, 697–706. http://dx.doi.org/10.1017/S0305004108001126 Google Scholar
[10] Nasr-Isfahani, R. and Soltani Renani, S., Character contractibility of Banach algebras and homologicalproperties of Banach modules. Studia Math. 202 (2011), no. 3, 205–225. http://dx.doi.org/10.4064/sm202-3-1 Google Scholar
[11] Runde, V., Lectures on amenability. Lecture Notes in Mathematics, 1774, Springer-Verlag, Berlin, 2002.Google Scholar
[12] Sherbert, D. R., The structure of ideals and point derivations in Banach algebras of Lipschitz functions. Trans. Amer. Math. Soc. 111 (1964), 240–272. http://dx.doi.org/10.1090/S0002-9947-1964-0161177-1 Google Scholar
[13] Ülger, A., Some results about the spectrum of commutative Banach algebras under the weak topologyand applications. Monatsh. Math. 121 (1996), no. 4, 353–379. http://dx.doi.org/10.1007/BF01308725 Google Scholar
[14] Zhang, Y., Weak amenability of a class of Banach algebras. Canad. Math. Bull. 44 (2001), no. 4, 504–508. http://dx.doi.org/10.4153/CMB-2001-050-7 Google Scholar