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The Operator Amenability of Uniform Algebras

Published online by Cambridge University Press:  20 November 2018

Volker Runde
Volker Runde*
Affiliation:
Department of Mathematical and Statistical Sciences University of Alberta Edmonton, Alberta T6G 2G1, e-mail: vrunde@ualberta.ca website: http://www.math.ualberta.ca/∼runde/
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Abstract

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We prove a quantized version of a theorem by M. V. Sheĭnberg: A uniform algebra equipped with its canonical, i.e., minimal, operator space structure is operator amenable if and only if it is a commutative ${{C}^{*}}$-algebra.

Keywords

46H2046H2546J1046J4047L25uniform algebrasamenable Banach algebrasoperator amenabilityminimal operator space

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 4 , 01 December 2003 , pp. 632 - 634
Copyright
Copyright © Canadian Mathematical Society 2003

References

[E-R] Effros, E. G. and Ruan, Z.-J., Operator Spaces. Oxford University Press, 2000.Google Scholar
[G-J-W] Grønbæk, N., Johnson, B. E. and Willis, G. A., Amenability of Banach algebras of compact operators. Israel J. Math. 87 (1994), 289–324.Google Scholar
[Joh 1] Johnson, B. E., Cohomology in Banach algebras. Mem. Amer. Math. Soc. 127(1972).Google Scholar
[Joh 2] Johnson, B. E., Non-amenability of the Fourier algebra of a compact group. J. London Math. Soc. (2).Google Scholar
[Rua 1] Ruan, Z.-J., The operator amenability of A(G). Amer. J. Math. 117 (1995), 1449–1474.Google Scholar
[Rua 2] Ruan, Z.-J., Amenability of Hopf-von Neumann algebras and Kac algebras. J. Funct. Anal. 139 (1996), 466–499.Google Scholar
[Run] Runde, V., Lectures on Amenability. Lecture Notes in Math. 1774, Springer Verlag, 2002.Google Scholar
[Sheĭ] Sheĭnberg, M. V., A characterization of the algebra C(Ω) in terms of cohomology groups (in Russian). Uspekhi Mat. Nauk 32 (1977), 203–204.Google Scholar