Geodesic
The Operator Amenability of Uniform Algebras
Canadian mathematical bulletin, Tome 46 (2003) no. 4, pp. 632-634

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2003-058-6
Mots-clés : 46H20, 46H25, 46J10, 46J40, 47L25, uniform algebras, amenable Banach algebras, operator amenability, minimal operator space 
Runde, Volker. The Operator Amenability of Uniform Algebras. Canadian mathematical bulletin, Tome 46 (2003) no. 4, pp. 632-634. doi: 10.4153/CMB-2003-058-6
@article{10_4153_CMB_2003_058_6,
     author = {Runde, Volker},
     title = {The {Operator} {Amenability} of {Uniform} {Algebras}},
     journal = {Canadian mathematical bulletin},
     pages = {632--634},
     year = {2003},
     volume = {46},
     number = {4},
     doi = {10.4153/CMB-2003-058-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-058-6/}
}
TY  - JOUR
AU  - Runde, Volker
TI  - The Operator Amenability of Uniform Algebras
JO  - Canadian mathematical bulletin
PY  - 2003
SP  - 632
EP  - 634
VL  - 46
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-058-6/
DO  - 10.4153/CMB-2003-058-6
ID  - 10_4153_CMB_2003_058_6
ER  - 
%0 Journal Article
%A Runde, Volker
%T The Operator Amenability of Uniform Algebras
%J Canadian mathematical bulletin
%D 2003
%P 632-634
%V 46
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-058-6/
%R 10.4153/CMB-2003-058-6
%F 10_4153_CMB_2003_058_6

[E-R] [E-R] Effros, E. G. and Ruan, Z.-J., Operator Spaces. Oxford University Press, 2000. Google Scholar

[G-J-W] [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] [Joh 1] Johnson, B. E., Cohomology in Banach algebras. Mem. Amer. Math. Soc. 127(1972). Google Scholar

[Joh 2] [Joh 2] Johnson, B. E., Non-amenability of the Fourier algebra of a compact group. J. London Math. Soc. (2). Google Scholar

[Rua 1] [Rua 1] Ruan, Z.-J., The operator amenability of A(G). Amer. J. Math. 117 (1995), 1449–1474. Google Scholar

[Rua 2] [Rua 2] Ruan, Z.-J., Amenability of Hopf-von Neumann algebras and Kac algebras. J. Funct. Anal. 139 (1996), 466–499. Google Scholar

[Run] [Run] Runde, V., Lectures on Amenability. Lecture Notes in Math. 1774, Springer Verlag, 2002. Google Scholar

[Sheĭ] [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

Cité par Sources :