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A NEW PROOF OF THE AMENABILITY OF C(X)

Published online by Cambridge University Press:  13 January 2010

MORTAZA ABTAHI*
Affiliation:
Department of Mathematics, Damghan University of Basic Sciences, Damghan 3671641167, Iran (email: [email protected])
YONG ZHANG
Affiliation:
Department of Mathematics, University of Manitoba, R3T 2N2, Canada (email: [email protected])
*
For correspondence; e-mail: [email protected]
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Abstract

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In this paper, we present a constructive proof of the amenability of C(X), where X is a compact space.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

[1]Dales, H. G., Banach Algebras and Automatic Continuity, LMS Monographs, 24 (Clarenden Press, Oxford, 2000).Google Scholar
[2]Ghahramani, F. and Loy, R. J., ‘Genaralized notions of amenability’, J. Funct. Anal. 208 (2004), 229260.CrossRefGoogle Scholar
[3]Ghahramani, F. and Zhang, Y., ‘Pseudo-amenable and pseudo-contractible Banach algebras’, Math. Proc. Cambridge Philos. Soc. 142 (2007), 111123.CrossRefGoogle Scholar
[4]Helemskii, A. Ya., Banach and Locally Convex Algebras (Oxford University Press, Oxford, 1993).CrossRefGoogle Scholar
[5]Johnson, B. E., Cohomology in Banach Algebras, Memoirs of the American Mathematical Society, 127 (American Mathematical Society, Providence, RI, 1972).CrossRefGoogle Scholar
[6]Johnson, B. E., ‘Approximate diagonals and cohomology of certain annihilator Banach algebras’, Amer. J. Math. 94 (1972), 685698.CrossRefGoogle Scholar
[7]Rudin, W., Real and Complex Analysis (McGraw-Hill, New York, 1987).Google Scholar