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Pseudo-amenable and pseudo-contractible Banach algebras

Published online by Cambridge University Press:  12 February 2007

F. GHAHRAMANI
Affiliation:
Department of Matematics, University of Manitoba, Winnipeg R3T 2N2, Canada. e-mail: [email protected], [email protected]
Y. ZHANG
Affiliation:
Department of Matematics, University of Manitoba, Winnipeg R3T 2N2, Canada. e-mail: [email protected], [email protected]

Abstract

We introduce and study two new notions of amenability for Banach algebras. In particular we compare these notions with some of those studied earlier. We show that several classes of Banach algebras, including certain Banach algebras related to locally compact groups, are responsive to these notions.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2007

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References

REFERENCES

[1] Bade, W. G., Curtis, P. C. and Dales, H. G.. Amenability and weak amenability for Beurling and Lipschitz algebras. Proc. London Math. Soc. 55 (1987), 359377.CrossRefGoogle Scholar
[2] Bonsall, F. F. and Duncan, J.. Complete Normed Algebras (Springer-Verlag, 1973).CrossRefGoogle Scholar
[3] Curtis, P. C. Jr. and Loy, R. J.. The structure of amenable Banach algebras. J. London Math. Soc. 40 (1989), 89104.CrossRefGoogle Scholar
[4] Dales, H. G.. Banach Algebras and Automatic Continuity (Oxford, 2000).Google Scholar
[5] Dales, H. G., Ghahramani, F. and Grønbæk, N.. Derivations into Iterated Duals of Banach Algebras. Studia Math. 128 (1998), 1954.Google Scholar
[6] Dales, H. G., Loy, R. J. and Zhang, Y.. Approximate amenability for Banach sequence algebras. Preprint (2005).CrossRefGoogle Scholar
[7] Ghahramani, F. and Lau, A. T. M.. Weak amenability of certain classes of Banach algebras without bounded approximate identities. Math. Proc. Camb. Phil. Soc. 133 (2002), 357371.CrossRefGoogle Scholar
[8] Ghahramani, F. and Loy, R. J.. Generalized notions of amenability. J. Funct. Anal. 208 (2004), 229260.CrossRefGoogle Scholar
[9] Ghahramani, F., Loy, R. J. and Zhang, Y.. Generalized notions of amenability, II. In preparation.Google Scholar
[10] Helemskii, A. Ya.. Banach and Locally Convex Algebras (Oxford University Press, 1993).CrossRefGoogle Scholar
[11] Helemskii, A. Ya.. Homological essence of amenability in the sense of A. Connes: the injectivity of the predual bimodule. Mat. Sb. 180 (1989), 16801690, 1728; Math. USSR-Sb. 68 (1991), 555–566.Google Scholar
[12] Hewitt, E. and Ross, K. A.. Abstract Harmonic Analysis II (Springer-Verlag, 1970).Google Scholar
[13] Johnson, B. E.. Cohomology in Banach algebras. Mem. Amer. Math. Soc. 127 (1972).Google Scholar
[14] Johnson, B. E.. Approximate diagonals and cohomology of certain annihilator Banach algebras. Amer. J. Math. 94 (1972), 685698.CrossRefGoogle Scholar
[15] Johnson, B. E., Kadison, R. V. and Ringrose, J.. Cohomology of operator algebras. III. Reduction to normal cohomology. Bull. Soc. Math. France 100 (1972), 7396.CrossRefGoogle Scholar
[16] Kotzmann, E. and Rindler, H.. Segal algebras on non-abelian groups. Trans. Amer. Math. Soc. 237 (1978), 271281.CrossRefGoogle Scholar
[17] Palmer, T. W.. Banach Algebras and the General Theory of *-Algebras, Vol. II (Cambridge, 2001).CrossRefGoogle Scholar
[18] Reiter, H.. L1-algebras and Segal Algebras. Lecture Notes in Math. 231 (Springer, 1971).CrossRefGoogle Scholar
[19] Reiter, H. and Stegeman, J. D.. Classical harmonic analysis and locally compact groups. London Math. Soc. Monogr. 22 (2000).Google Scholar
[20] Willis, G. A.. Approximate units in finite codimensional ideals of group algebras. J. London Math. Soc. 26 (1982), 143154.CrossRefGoogle Scholar
[21] Zhang, Y.. Nilpotent ideals in a class of Banach algebras. Proc. Amer. Math. Soc. 127 (1999), 32373242.CrossRefGoogle Scholar
[22] Zhang, Y.. Maximal ideals and the structure of contractible and amenable Banach algebras. Bull. Austral. Math. Soc. 62 (2000), 221226.CrossRefGoogle Scholar
[23] Zhang, Y.. Approximate complementation and its applications in studying ideals of Banach algebras. Math. Scand. 92 (2003), 301308.CrossRefGoogle Scholar